Multiplying and Dividing Rational Expressions Chapter 5.4

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

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

Simplify Rational Expressions – Pg. 327

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

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

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

Multiplying Rational Expressions – Pg. 329

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 5 15 𝑥 4 𝑦

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

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)

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)