The document provides an overview of rational expressions, defining them as expressions that can be written in the form of fractions where both the numerator and denominator are polynomials. It includes objectives such as evaluating these expressions and identifying variable values that render the expressions undefined. Additionally, it offers examples and exercises to illustrate the evaluation process and determination of undefined expressions.

1. Let’s have Fun!

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A T

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P R S N

4. Rational Expressions
Objectives:
define rational expressions
Evaluate rational expressions; and
Find every value of the variables in the
denominator that makes a rational
expression undefined.

5. Where Do I Belong?
Rational
Expressions
Not Rational
Expressions

6. Where Do I Belong?
Not Rational
Expressions
𝑥
2
+7 5 𝑘
2(0)
𝑐
5+7(𝐶)
𝑛− 2
𝑛
𝑥 6
𝑝− 𝑝
𝑥 2− 9
𝑥
𝑏
2− 0
𝑥 +6
0

7. Rational Expressions
Definition
A rational expression in one variable is an
expression that can be written in the form
where P and Q are polynomials in one variable
and Q

8. Rational Expressions
Remember that in evaluating algebraic
expressions, we replace the variables with the
given values and then simply the resulting
expression.

9. Evaluate
Evaluate the expression when
Example 1
a. x=0
b. x=1
x=
x= 2

10. Evaluate
Find every value of the variable that
makes each expression undefined.
Example #2
a. b.

11. Evaluate
To make rational expression undefined,
equate the denominator to zero and solve
for the variable.
Solution

12. Evaluate
Solution
a. Equate the denominator to 0
Add 3 on both sides
The expression is undefined if a is replaced by 3
because the denominator would be 0.

13. Evaluate
Solution
Equate the denominator to 0
Add b on both sides
The expression is undefined if variables a and b
are replaced by equal values.
b.

14. Evaluate
Find every value of the variable that makes
each expression undefined .
Try it #2
a. b.