Powerpoint presentation on rational equations

Objectives
At the end of this lesson, the learner should be able to
● accurately define a rational equation, and solutions
and extraneous solutions of rational equations; and
● correctly solve rational equations.

Essential Questions
● What are rational equations?
● How do you solve rational equations?
● What is an extraneous solution of a rational equation?

Warm Up!
Before we learn how to solve rational equations, let us recall
how to get the least common multiple of polynomials by
watching a short clip.
(Click on the link to access the video clip)
“Finding LCM of Polynomials”. EvCCMath.
Retrieved 22 February 2019 from
https://www.youtube.com/watch?v=1E4foCjeNGw&feature=s
hare

Guide Questions
● How do we factor polynomials?
● How do you solve for the least common multiple of two
polynomials?
● When can we apply the process of finding the LCM of two
or more polynomials?
● What do we call the fractions that contain polynomial
expressions?

Learn about It!
Rational Expression
is a fraction whose numerator and denominator are both polynomials. It can be
written in the form , where and are both polynomials, and .
1
Examples:

Learn about It!
2 Rational Equation
is an equation whose terms are rational expressions.
Examples:

Learn about It!
3 Least Common Denominator
is the least common multiple of the denominators.
Example:
The LCD of the rational expressions and is
.

Learn about It!
4 Solutions (or roots)
values that satisfy a given rational equation.
Example:
The value is a solution of the rational expression
.

Learn about It!
5 Extraneous Solutions
values that arrived at upon solving a rational equation but do not satisfy the given
equation.
Example:
In solving , will be equal to 2 and 3. However, 2 is an
extraneous solution since using 2 as a value of makes the
denominator equal to zero; thus, the rational expression
will be undefined.

Try It!
Example 1: Solve .
Solution:
1. Find the LCD.
The denominators are and . Both of these
expressions are completely factored already. Thus, the
LCD
of the terms of the equation is .

Try It!
2. Multiply both sides of the equation by the LCD to remove
the denominators then solve for the unknown variable.
(𝟑) ( 𝒙+𝟏)( 𝑥
𝑥+1 )=(4
3 )(𝟑) ( 𝒙+𝟏 )
3 𝑥=4 𝑥+4
Example 1: Solve .
− 𝑥=4
𝑥=− 4

Try It!
3. Verify your answer by substituting to the original
equation. Then, simplify.
Example 1: Solve .
− 4
−3
=
4
3
4
3
=
4
3
?
?


Try It!
Since it satisfies the equation, is the solution or root of the given
equation.
Example 1: Solve .

Try It!
Example 2: Find the solution/s of .
Solution:
1. Find the LCD.
The denominators are and . Both of these
expressions are completely factored already. Thus, the
LCD of the given equation is .

Try It!
2. Multiply both sides of the equation by the LCD to remove
the denominators then solve for the unknown variable.
(𝟑) ( 𝒚 +𝟒)( 4
𝑦+4 )=(𝑦
3 )(𝟑)( 𝒚 +𝟒)
12= 𝑦2
+4 𝑦

Try It!
Hence,
12= 𝑦2
+4 𝑦
− 𝑦2
− 4 𝑦+12=0
𝑦2
+4 𝑦+12=0
( 𝑦+6) ( 𝑦 − 2)=0

Try It!
3. Verify your answer by substituting each obtained solution
to the original equation.
For :
Since it satisfies the equation, is a solution or root of the
given equation.
4
−6+4
=
−6
3
4
−2
=
−6
3 −2=−2
? 
?

Try It!
For :
Since it satisfies the equation, is also a solution or root of
the given equation.
Therefore, and are the solutions or roots of the given
equation.
4
2+4
=
2
3
4
6
=
2
3
2
3
=
2
3
? 
?

Let’s Practice!
Individual Practice:
1. Solve .
2. Solve .

Let’s Practice!
Group Practice: To be done in pairs.
1. Andres bought 60 kilograms of fruits consisting of
pomelo and seedless red grapes. He bought ₱4800 worth
of pomelo and ₱8400 worth of seedless red grapes. If the
cost per kilogram of seedless red grapes is ₱30 less than
that of pomelo, how many kilograms of each fruit did he
buy?

Key Points
1
2
Rational Expression
is a fraction whose numerator and denominator are both polynomials. It can be written in
the form , where and are both polynomials, and .
Rational Equation
is an equation whose terms are rational expressions.
3 Least Common Denominator
is the least common multiple of the denominators.

Key Points
1
2
4 Root or Solution
values that satisfy a given rational equation.
5
Extraneous Root or Solution
values that arrived at upon solving a rational equation but do not satisfy the given
equation.

Synthesis
● How do you solve rational equations?
● Why are rational equations important in our lives?
● What are some applications of rational equations?

Powerpoint presentation on rational equations

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