1. Multiplying and Dividing Rational Expressions
Chapter 5.4

2. Review of Factoring
10𝑥− 5𝑥 2
𝑥 2 −49
𝑥 2 −2𝑥−48
𝑥 3 −125

3. Vocabulary
Simplified form – a rational expression is in simplified form if its numerator and denominator have no common factors.
Reciprocal – “flip it”

4. Simplify Rational Expressions – Pg. 327

5. Simplify each expression.
2 𝑥+1 𝑥+1 𝑥+3
𝑥 2 −2𝑥−15 𝑥 2 −9
𝑥 2 −8𝑥+16 𝑥 2 +2𝑥−24

6. Simplify each expression.
4. 𝑥 2 +11𝑥+28 2 𝑥 2 +8𝑥
5. 𝑥 𝑥 2 −𝑥−12
6. 𝑥 3 −27 𝑥 2 −9

7. Simplify each expression.
7. 𝑥+4 𝑥 2 −16
8. 𝑥 2 −2𝑥−3 𝑥 2 −𝑥−6

8. Multiplying Rational Expressions – Pg. 329

9. Multiply each expression. Simplify your result.
8 𝑥 3 𝑦 2𝑥 𝑦 2 ∙ 7 𝑥 4 𝑦 3 4𝑦
5 𝑥 2 𝑦 3 3𝑥 𝑦 4 ∙ 27 𝑥 𝑥 4 𝑦

10. Multiply each expression. Simplify your result.
3. 3𝑥− 3𝑥 2 𝑥 2 +4𝑥−5 ∙ 𝑥 2 +𝑥−20 3𝑥
𝑥− 5𝑥 2 𝑥 2 −𝑥 ∙ 𝑥 2 +3𝑥−4 𝑥 2 −16

11. Multiply each expression. Simplify your result.
5. 𝑥+2 𝑥 3 −27 ∙( 𝑥 2 +3𝑥+9)
6. 𝑥+5 𝑥 3 −1 ∙( 𝑥 2 +𝑥+1)

12. Divide Rational Expressions
7𝑥 2𝑥−10 ÷ 𝑥 2 −6𝑥 𝑥 2 −11𝑥+30
𝑥 2 −4𝑥−21 5𝑥+15 ÷ 𝑥 2 +3𝑥−70 𝑥 2 −100
6𝑥 2 +𝑥−15 4𝑥 2 ÷(3 𝑥 2 +5𝑥)