1. The document discusses solving algebraic equations. It provides 10 examples of solving linear, quadratic, and literal equations with step-by-step solutions.
2. The examples cover a range of solution methods including factoring, combining like terms, and using the lowest common multiple.
3. The final 3 questions involve solving systems of linear equations, determining values that make equations incompatible, and calculating the value of a variable.
Sesión de aprendizaje de matemática para 2 año de secundariaAlicia Cruz Ccahuana
se ha usado un modelo de las sesiones de reforzamiento y se ha incorporado la direcciones o hipervínculos, para poder ayudar a comprender el tema de fracciones usando diapositivas.
Sesión de aprendizaje de matemática para 2 año de secundariaAlicia Cruz Ccahuana
se ha usado un modelo de las sesiones de reforzamiento y se ha incorporado la direcciones o hipervínculos, para poder ayudar a comprender el tema de fracciones usando diapositivas.
1) Use properties of logarithms to expand the following logarit.docxhirstcruz
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Log
b
(√xy
3
/ z
3
)
A. 1/2 log
b
x - 6 log
b
y + 3 log
b
z
B. 1/2 log
b
x - 9 log
b
y - 3 log
b
z
C. 1/2 log
b
x + 3 log
b
y + 6 log
b
z
D. 1/2 log
b
x + 3 log
b
y - 3 log
b
z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2
-4
= 1/16
A. Log
4
1/16 = 64
B. Log
2
1/24 = -4
C. Log
2
1/16 = -4
D. Log
4
1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log
2
96 – log
2
3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A
0
e
kt
, to show that the time it takes a population to double (to grow from A
0
to 2A
0
) is given by t = ln 2/k.
A. A
0
= A
0
e
kt
; ln = e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
B. 2A
0
= A
0
e; 2= e
kt
; ln = ln e
kt
; ln 2 = kt; ln 2/k = t
C. 2A
0
= A
0
e
kt
; 2= e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
D. 2A
0
= A
0
e
kt
; 2 = e
kt
; ln 1 = ln e
kt
; ln 2 = kt; ln 2/k = t
oe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
log
b
(x
2
y) / z
2
A. 2 log
b
x + log
b
y - 2 log
b
z
B. 4 log
b
x - log
b
y - 2 log
b
z
C. 2 log
b
x + 2 log
b
y + 2 log
b
z
D. log
b
x - log
b
y + 2 log
b
z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3
√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log
2
16
A. 2 log
4
= 16
B. 2
2
= 4
C. 4
4
= 256
D. 2
4
= 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
3
1-x
= 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the followin.
1) Use properties of logarithms to expand the following logarithm.docxdorishigh
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Logb (√xy3 / z3)
A. 1/2 logb x - 6 logb y + 3 logb z
B. 1/2 logb x - 9 logb y - 3 logb z
C. 1/2 logb x + 3 logb y + 6 logb z
D. 1/2 logb x + 3 logb y - 3 logb z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2-4 = 1/16
A. Log4 1/16 = 64
B. Log2 1/24 = -4
C. Log2 1/16 = -4
D. Log4 1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log2 96 – log2 3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k.
A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t
C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2 y) / z2
A. 2 logb x + logb y - 2 logb z
B. 4 logb x - logb y - 2 logb z
C. 2 logb x + 2 logb y + 2 logb z
D. logb x - logb y + 2 logb z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log2 16
A. 2 log4 = 16
B. 22 = 4
C. 44 = 256
D. 24 = 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2y)
A. 2 logy x + logx y
B. 2 logb x + logb y
C. logx - logb y
D. logb x – ...
1. Factor completely. 9x2 + 30xy + 25y2
a. (3x + 5y)2
b. (3x – 5y)(3x + 5y)
c. (9x + 5y)(x + 5y)
d. (3x + y)(3x + 25y)
2. During rush hour, Fernando can drive 25 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If
Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.
a. 36
b. 38
c. 45
d. 47
3. Factor the trinomial completely.. 6b4 – 18b3 – 60b2
a. 6b2(b + 2)(b – 5)
b. 6b2(b – 2)(b + 5)
c. 6(b2 + 2)(b2 – 5)
d. b2(2b + 5)(3b + 10)
4.
Solve for x.
a. –2
b. 2
c. –4
d. No solution
5. The directions on a concentrated cleaner state that 3 tablespoons of concentrate make 345 ounces of cleaning fluid. How many ounces of
cleaning fluid will 2 tablespoons of cleaner make?
a. 190
b. 210
c. 230
d. 250
6. The profit on a watch is given by P = x2 – 13x – 80, where x is the number of watches sold per day. How many watches were sold on a day when
there was a $50 loss?
a. 13
b. 14
c. 15
d. 16
7. The area of a rectangle of length t is given by 12t – t2. Find the width of the rectangle in terms of t.
a. 12 – t
b. 12t
c. t – 12
d. t2
8.
Write in simplest form.
a.
b.
c.
d.
9. State which method should be applied as the first step for factoring the polynomial. (x + 9y)2 – 1
a. Find the GCF.
b. Group the terms.
c. Factor the difference of squares.
d. Use the ac method (or trial and error).
10.
Write the expression in simplest form.
a.
b. -
c. -
d.
11. Factor 3x3-x-4
a. (3x-4)(x+1)
b. (3x+4)(x+1)
c. (3x-4)(x-1)
d. (3x+4)(x 1)
12. Determine whether the following trinomial is a perfect square. If it is, factor the binomial. x2 + 9x + 9
a. Yes; (x + 3)2
b. Yes; (x – 3)2
c. Yes; (x + 9)2
d. No
13. What values for x, if any, must be excluded in the following algebraic fraction?
a.
b.
c.
d.
14. The volume V of a hollow cylinder is given by the formula V = L(R22 – R12). Factor the right-hand side of this equation.
a. L(R2 + R1)
2
b. L(R2 – R1)
2
c. L(R2 + R1)(R2 – R1)
d. LR2(R2 – R1)
15. Solve the quadratic equation. x2 = –6x
a. 0, –6
b. 0, 6
c. 6, –6
d. 2, 6
16.
Add. Express your result in simplest form.
a.
b.
c.
d.
17.
Multiply.
a.
b.
c. –n2 + n
d. 3
18.
Add or subtract as indicated.
a.
b.
c.
d.
19. One number is 8 more than another. Let x represent the larger number and use a rational expression to represent the sum of the reciprocals of
the two numbers.
a. 1
b.
c.
d.
20.
Write in simplest form.
a.
b.
c. 4a4b
d.
21.
Multiply.
a.
b.
c.
d.
22.
Simplify.
a.
b.
c.
d.
23. Factor completely. 15x2 – 16x + 4
a. (3x – 2)(5x – 2)
b. (3x + 2)(5x + 2)
c. (15x – 2)(x – 2 ...
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
2. A) a+b B) a-b C) b-a D) a E) b
1. Resolver:
Rpta. C
Solución
2
a
b
x
b
a
x
2
a
b
x
b
a
x
a(x + a) – b (x – b) = 2ab
ax + a2 – bx + b2 =2ab
a2 + b2 – 2ab = x(b – a)
(a – b)2 = (b – a)2 =x(b – a)
x = b – a
MCM = ab
3. A) 1 B) 2 C) 3 D) 4 E) 5
2. Resolver:
Rpta. E
Solución
2
6
5
3
2
x
x
x
2
6
5
3
2
x
x
x
2
6
10
6
5
x
x
x
30
5
6
5
x
x
x
30
6
x
5
x
Método Práctico
4. A) 1/5 B) 2/5 C) 3/5 D) 4 /5 E) 6/5
3.
Rpta. D
Solución
Qué valor de x satisface la ecuación:
Siendo el MCM (4, 3, 6) = 12, se obtiene:
6
7
x
2
3
1
x
5
4
2
x
3
6
7
x
2
3
1
x
5
4
2
x
3
3 ( 3x – 2 ) – 4 ( 5x – 1 ) = 2 ( 2x – 7 )
9x – 6 – 20x + 4 = 4x – 14
– 15x = – 12 15
12
x
5
4
x
5. Solución
4. Resolver:
Rpta. B
A) 1 B) 2 C) 3 D) 4 E) 7
6
3
3
1
2
1
2
x
x
x
x
6
3
3
1
2
1
2
x
x
x
x
6
3
2
2
x
x
x
x
6
3
2
x
x
3
1
2
x
2
x
4
2
x
Método Práctico
6. Solución
5. Resolver:
Rpta. C
A) 𝟕 B) 8 C) 9 D) 10 E) 11
6 2x 2x 2
x 1
3 5
6 2x 2x 2
x 1
3 5
)
2
2
(
3
)
1
(
15
)
2
6
(
5
x
x
x
6
6
15
15
10
30
x
x
x
x
9
MCM = 15
7. Solución
6. Resolver:
Rpta. A
1
1
1
x
b
a
b
x
a
b
a
1
1
1
x
b
a
b
x
a
b
a
a2x – a3 + b2x – b3 = abx
a2x – abx + b2x = a3 + b3
x(a2– ab + b2) = a3 + b3
2 2 3 3
a b . a ab b a b
x = a+b
A) a+b B) a-b C) b-a D) a E) b
MCM = abx
1
x
b
x
a
b
x
a
x
b
a
8. Solución
7. Resolver:
Rpta. C
A) 1 B) 4 C) 5 D) 15 E) 1/5
7 x 9 x 2x 7 x 1
2 4 3 6
7 x 9 x 2x 7 x 1
2 4 3 6
8
2
18
4
28 x
x
18
3
3
42
12
x
x
4
3
23 x
6
13
5
x
26
10
9
69
x
x 5
x
2
3
23 x
3
13
5
x
x
19
95
Método Práctico
9. Solución
8.
Rpta. E
b
a
b
b
x
a
a
x
a
b
x
b
a
x
2
2
Resolver la ecuación literal:
b
a
b
x
a
a
x
b
b
x
b
a
x
a
)
2
(
)
2
(
)
(
)
(
En las fracciones, siendo el MCM (b, a, a, b) = ab; se tendría:
b
a
ab
ax
ab
bx
a
bx
a
ax
2
2
2
2
b
a
x
b
a
b
a
b
a
x
b
a
b
a
x
b
a
b
a
x
b
a
)
(
)
)(
(
)
(
)
(
)
(
)
( 2
2
ax
b
b
a
bx
b
a
x
b
a
x
)
(
)
(
(a + b)x=ab+b2 =b(a + b)
x=b
A) a+b B) a-b C) b-a D) a E) b
11. Solución
10.
Rpta. D
A) 2 B) − 2 C) 1 D) − 1 E) 4
x
5
2
x
1
4
3
2
5
3
x
1
x
1
4
3
2
5
Qué valor de x satisface :
Debe tenerse en cuenta que los términos que son iguales en los dos
miembros de la ecuación se pueden cancelar directamente; es decir: 5 con 5;
2 con 2; 3 con 3; -4 con –4 y 1 con 1; quedando:
x
5
2
x
3
x
1
x
5
x
2
x
3
x
1
x
X2 – 5x – x + 5=x2 – 2x – 3x + 6
– x+5=6 x = – 1
Equivalente:
12. Solución
11. Resolver:
Rpta. E
A) 13a/5 B) 13a/50 C) 13a D) 2a/15 E) 13a/60
2
3
a
x
5
a
x
5
a
x
5
a
x
5
n
a
x
5
m
a
x
5
Haciendo el cambio de variable:
n
3
m
3
n
2
m
2
2
3
n
m
n
m
La ecuación se transforma en: 5n = m
a
x
5
a
x
5
5
volviendo a la variable original
25(5x-a) = 5x+a
125x-25a = 5x+a
elevando al cuadrado
120 x = 26a
60
13a
X
13. Solución
12.
Rpta. B
A) 1 B) 2 C) 3 D) 4 E) 5
2
2
2
7
x
3
x
10
x
6
x
50
x
14
x
Calcular “x” en la ecuación:
Transformando el exponente negativo en positivo y desarrollando el
cuadrado del binomio obtenemos:
2
2
2
3
7
10
6
50
14
x
x
x
x
x
x
9
x
6
x
49
x
14
x
10
x
6
x
50
x
14
x
2
2
2
2
x2–14x+49 = a
x2+6x+9=b
b
a
1
b
1
a
ab + b=ab + a
b = a
x2+6x+9 = x2 –14x+49
X = 2
14. Solución
13.
Rpta. E
A) 6/5 B) 7/5 C) 8/5 D) – 6/5 E) – 8/5
2x + ky = 5 k ........... ()
5x – 4 y = -27 ……….. (ß)
Dado el sistema:
8
K
5
K
7
K
5
8
K
27
k
20
4
5
k
2
4
27
k
k
5
x
Calculando “x”, vemos que:
Para que no exista solución(incompatible)
debe cumplirse que: – 5 k – 8 = 0
5
8
K
para que valor de “K”
es incompatible
15. Solución
14.
Rpta. D
A) 60 B) 65 C) 70 D) 75 E) 80
30
5
2
3
4
5
2
5
2
2
3
1
x
x
x
x
x
Resuelve la siguiente ecuación:
5
150
x
4
x
5
5
2
10
x
9
3
1
30
5
2
3
4
5
2
5
2
2
3
1
x
x
x
x
x
10
300
x
2
10
x
5
10
x
3
– 4x = – 300
75
X
Método Práctico
18. Solución
1. Resolver:
Rpta. B
0
a
b
x
b
x
a
A) a+b B) a-b C) b-a D) a E) b
0
a
b
x
b
x
a
b
a
x
b
a
b
a
b
a
x
x
a
b
b
a
b
bx
ax
a
b
x
b
x
a
a
2
2
2
2
Trasponiendo
19. Solución
2.
Rpta. C
Resolver:
A) b B) 2b C) 3b D) 4b E) 5b
b
a
b
x
b
a
b
x
b
a
b
a
b
a
a
x
b
a
b
x
b
a
b
x
b
a
b
a
b
a
a
x
b
a
b
a
b
a
b
x
b
a
b
x
b
a
a
x
b
a
b
b
a
x
b
a
b
a
)
(
b
a
b
b
a
x
b
a
b
a
)
(
b
b
a
x
a
b
b
x 3
Trasponiendo
20. Solución
3. Resolver:
Rpta. E
A) 1/2 B) – 1/3 C) 1/5 D) 1/4 E) – 1/5
2
1
1
x
1
x
1
1
x
1
x
1
x
1
x
2
1
1
x
1
x
1
1
x
1
x
1
x
1
x
2
1
1
)
1
(
1
)
1
)(
1
(
)
1
)(
1
(
)
1
)(
1
(
x
x
x
x
x
x
x
x
x
2
1
)
1
(
2
4
x
x
1
4
x
x
5
1
x
21. Solución
4.
Rpta. C
3𝑥 + 11
𝑥2 + 7𝑥 + 12
=
𝐴
𝑥 + 4
+
𝐵
𝑥 + 3
Calcular el valor de A+B en:
A) 1 B) 2 C) 3 D) 4 E) 7
3𝑥 + 11
𝑥2 + 7𝑥 + 12
=
𝐴
𝑥 + 4
+
𝐵
𝑥 + 3
3𝑥 + 11
𝑥2 + 7𝑥 + 12
=
𝐴 𝑥 + 3 + 𝐵(𝑥 + 4)
(𝑥 + 4)(x + 3)
3x + 11= A x + 3 + B X + 4 = A + B x + (3A + 4B)
A+B = 3
3A+4B = 11
A = 1 B = 2 A+B = 3
22. 5. Al resolver:
Rpta. E
A) − 1 B) 3 C) 2 D) 1 E) 0
2
1
2
1
1
2
1
1
1
x
2
1
2
1
1
2
1
1
1
x
1
1
2
1
1
2
1
1
x
1
1
2
1
1
x
x
1
2
1
1
2
1
2
1
2
1
x
2
1
2
3
x
1
3
2
x
Solución
Hallar el valor de
E = 3X – 2
0
2
)
3
2
(
3
E
23. Solución
6. Resolver:
Rpta. E
A) mn B) m+n C) m− n D) E)
1
x m x n
m n
n(x + m) + m (x + n) = mn
nx + mn + m x + mn = mn
x(m + n) = − mn
n
m
mn
x
n
m
mn
n
m
mn
1
x m x n
m n
MCM = mn