a power point presention for multiplying and dividing expressions

1. Simplifying
Multiplying
Dividing
Grade 9 B – T3 -W 5- 13/14

2. Simplifying

3. Remember, denominators
can not = 0.
Now,lets go through the steps to
simplify a rational expression.
Examples of rational expressions
2
4 8 4 7
, ,
3 3 5 9
x y
x x y y
 
  

4. Simplify:
7x  7
x
2
1
Step 1: Factor the numerator and
the denominator completely looking
for common factors.
7x  7  7(x 1)
x2
1  (x 1)(x 1)
Next

5. 7x  7
x
2
1

7(x 1)
(x 1)(x 1)
What is the common factor?
x1
Step 2: Divide the numerator and
denominator by the common factor.

6. 7(x 1)
(x  1)(x 1)

7(x 1)
(x  1)(x 1)
1
1
Step 3: Multiply to get your answer.
Answer:
7
x 1

7. Looking at the answer from the
previous example, what value of x
would make the denominator 0?
x= -1
The expression is undefined when the
values make the denominator equal to 0

8. How do I find the values
that make an expression
undefined?
Completely factor the original
denominator.

9. Ex:
2ab(a  2)(b  3)
3ab(a
2
 4)
3ab(a
2
 4)  3ab(a  2)(a  2)
The expression is undefined when:
a= 0, 2, and -2 and b= 0.
Factor the denominator

10. Lets go through another example.
3a3
 a4
2a
3
 6a
2
3a3
 a4
2a
3
 6a
2 
a3
(3 a)
2a
2
(a 3)
Factor
out the
GCF
Next

11. 3
2
2 ( 3)
(3 )a
a a
a


  3 factored is 1( 3)a a  
cancel like factors
3
2
1 ( 3)
2 ( 3)
a a
a a
 


1
1
3
2
1( 3)
2 ( 3)
a
a a
a

 


12. 3
2
1
2
a
a
 2
cancel out the like factor a
1
2
a
1
a
answer
What values is the original expression undefined?

13. Now try to do some on your own.
2
2
3 2
3 2
5 6
1)
9
5 10
2)
6 16
x x
x
x x
x x x
 


 
Also find the values that make
each expression undefined?

14. Multiplying and
Dividing

15. Multiplying and Dividing
Rational Expressions
Remember that a rational number
can be expressed as a quotient of
two integers. A rational expression
can be expressed as a quotient of
two polynomials.

16. Remember how to multiply fractions:
First you multiply the numerators
then multiply the denominators.
5 2
:
6 20
Ex 
10 1
120 12

5 2
6 20


17. The same method can be used
to multiply rational expressions.
Ex:
4a2
5ab
3 
3bc
12a
3 
4  a  a 3  b c
5 a  b  b b 12  a  a a
11 1 1 1
1 1 1 1

c
5b
2
a
2

18. Let’s do another one.
Ex:
x3
 3x2
x
2
 5x  6

x2
10x  9
x
2
 6x  27
Step #1: Factor the numerator
and the denominator.
x2
(x  3)
(x 6)(x 1)

(x 1)(x 9)
(x  9)(x 3)
Next

19. Step #2: Divide the numerator and
denominator by the common factors.
x2
(x  3)
(x 6)(x 1)

(x 1)(x 9)
(x  9)(x 3)
1
1
1
1
1
1

20. Step #3: Multiply the numerator
and the denominator.
x2
x  6
Remember how to divide fractions?

21. Multiply by the reciprocal of the
divisor. 4
5

16
25

4
5

25
16

4  25
516
1
1
5
4

5
4

22. Dividing rational expressions uses
the same procedure.
Ex: Simplify
y  2
y
2
10y  24

y2
 2y
y
2
 2y  8

23. y  2
y
2
10y  24

y2
 2y
y
2
 2y  8

y  2
y
2
10y  24

y2
 2y  8
y
2
 2y

y  2
(y 12)(y  2)

(y  4)(y  2)
y(y  2)

1 1
1 1
Next
4
( 12)
y
y y



24. Now you try to simplify the
expression:
x  3
x
2
 4x 12

2x2
 6x
x  2

25. Choose the correct answer .

26. Answer:
1
2x(x  6)
Now try these on your own.
1)
x + 3
2x3
 2x2

x2
 7x  6
x2
10x  21
2)
3x  6
7x  7

5x 10
14x 14