1. Look for common factors.
Simplify a Rational Expression
A. Simplify
Look for common factors.
Eliminate common factors. ●
Simplify.
Answer:
Example 1A

2. B. Under what conditions is the expression undefined?
Simplify a Rational Expression
B. Under what conditions is the expression undefined?
Just as with a fraction, a rational expression is undefined if the denominator equals zero.
The original factored denominator is (y + 7)(y – 3)(y + 3).
Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3.
Example 1B

3. For what value(s) of p is undefined? A 5 B –3, 5 C 3, –5 D 5, 1, –3
Undefined Values
For what value(s) of p is undefined?
A 5 B –3, 5
C 3, –5 D 5, 1, –3
Read the Test Item
You want to determine which values of p make the denominator equal to 0.
Example 2

4. p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator.
Undefined Values
Solve the Test Item
Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator.
p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator.
p – 5 = 0 or p + 3 = 0 Zero Product Property
p = 5 p = –3 Solve each equation.
Answer: B
Example 2

5. Factor the numerator and the denominator.
Simplify Using –1
Simplify
Factor the numerator and the denominator.
b – 2 = –(–b + 2) or –1(2 – b)
Simplify.
Answer: –a
Example 3

6. Concept

7. A. Simplify . Simplify. Simplify. Answer:
Multiply and Divide Rational Expressions
A. Simplify
Simplify.
Simplify.
Answer:
Example 4A

8. Multiply by the reciprocal of the divisor.
Multiply and Divide Rational Expressions
B. Simplify
Multiply by the reciprocal of the divisor.
Simplify.
Example 4B

9. Multiply and Divide Rational Expressions
Simplify.
Answer:
Example 4B

10. A. Simplify . Factor. 1 + k = k + 1, 1 – k = –1(k – 1) = –1 Simplify.
Polynomials in the Numerator and Denominator
A. Simplify
Factor.
1 + k = k + 1, 1 – k = –1(k – 1)
= –1 Simplify.
Answer: –1
Example 5A

11. Multiply by the reciprocal of the divisor.
Polynomials in the Numerator and Denominator
B. Simplify
Multiply by the reciprocal of the divisor.
Factor.
Example 5B

12. Simplify. Answer: Polynomials in the Numerator and Denominator
Example 5B

13. Express as a division expression.
Simplify Complex Fractions
Simplify
Express as a division expression.
Multiply by the reciprocal of the divisor.
Example 6

14. Simplify Complex Fractions
Factor. –1
Simplify.
Answer:
Example 6