Math

Name________________________________________________ Block_______________ Date_________________

Algebra II Unit 8a– Rational Functions - Review

Target

Obj 08A – I can simplify, multiply and divide algebraic expressions with common monomial or binomial factors

Obj 08b – I can add and subtract rational expressions with common monomial or binomial factors.

Simplify each rational expression below. State any restrictions on the variables.

1. 5𝑥3−45𝑥

10𝑥2(𝑥+3)(𝑥−3) 2.

5𝑥2−40𝑥

𝑥2−6𝑥−16 ÷

5𝑥

𝑥−5

3. 𝑥−4

3𝑥2−4𝑥−4 ∙ 7𝑥2−19𝑥+10

5𝑥−20

4. 𝑥2−49

𝑥2−25 ÷

3𝑥2+21𝑥

𝑥+5

4. Which expression can be simplified to 𝑥+2

𝑥−3 ? Select all that apply.

A. 𝑥2+6𝑥+8

𝑥2+𝑥−12 B.

𝑥2−3𝑥−2

𝑥2+2𝑥−3 C.

𝑥2−2𝑥−8

𝑥2−7𝑥+12 D.

𝑥2+5𝑥+4

𝑥2+7𝑥+12

5. Which is an equivalent form of this expression if defined.

2𝑥2

𝑥2 − 𝑥 − 42 ∙ 𝑥2 − 10𝑥 + 21

𝑥 − 3

A. 9𝑥

4 B. 6 C.

2𝑥2

𝑥+6

D. 5

Simplify each rational expression below.

5. 𝑘−1

𝑘+5 −

4

5

7. 𝑥

𝑥−2 +

𝑥−12

(𝑥+3)(𝑥−2)

8. 3

𝑥+1 +

𝑥

𝑥−1

9. 3𝑥

𝑥2−25 −

1

𝑥2−10𝑥+25