7.3 - Multiplying and Dividing Rational Expressions

Simplifying

100

(x²+3x-28) / (3x²+19x-14)

(x - 4) / (3x - 2)

200

(3x²+71x+46) / (9x²-4)

(x + 23) / (3x - 2)

300

Put your answer in factored form: (x⁴ - 16) / (x²+5x+6)

(x - 2)(x²+4) / (x + 3)

400

(x²-1)² / (x+1)

(x³) - x² - x+1

500

(x⁴ - 2x³ - 13x² + 14x +24) / (x² - 3x - 4)

x² + x - 6

Multiplying

100

[(4x² - 4x) / (x² + x – 42)] ∙ [(x² + 3x -28) / (4x)]

(x² - 5x + 4) / (x – 6)

200

[(x^3+2x²) / (x – 7)] · [(x² - 5x – 14) / x³]

[(x²+4x+4) / x]

300

[(x² + 5x – 6) / (x² + 6x + 9)] ∙ [(4x² + 12x) / (x² - 6x + 5)]

[(4x² + 24x) / (x² - 2x + 15)]

400

[(x² + 3x +2) / (4x² - 36)] ∙ (2x² - 4x – 6)

((x^3) + 4x² + 5x + 2) / (2x + 6)

500

Bobby Donald Jr. has just built a new garden. If the length is (x² + 7x + 12) / (x² + 8x + 16) inches and the width is (9x² + 12x) / (3x² + 9x) inches. What is the area of the space the garden takes up? Remember units count!

(3x + 4) / (x + 4) square inches

Dividing

100

[(y¹⁰) / 27(x³)(y²)] ÷ [(y⁸) / 3(x⁴)]

x / 9

200

[(x² +x – 6) / (x² + 7x + 6)] ÷ [(x² + 2x – 8) / (x² + 3x – 18)]

(x² - 9) / (x² + 5x + 4)

300

[(x² - 2x – 3) / (x + 5)] ÷ (x² + 2x + 1)

(x - 3) / (x² + 6x + 5)

400

[(x² + 8x – 20) / (x + 3)] ÷ (x² + 20x + 100)

(x – 2) / (x² + 13x + 30)

500

[(x² + 5x – 24) / (x² + x – 20)] ÷ [(x² +10x + 16) / (x² + 9x + 20)]

(x² + x – 12) / (x² - 2x – 8)

???

100

The denominator of a rational expression is factored into (2x + 3)(2x - 5)(x - 7). What are the restricted values of this expression?

x cannot be equal to -3/2, 5/2, or 7

200

The area of a rectangle is given by x² - 13x + 42. If its width is x - 7, what is its length?

x - 6

300

What set represents the values that x can take in the expression (x + 2)/(2x - 1)?

Answers may vary.

400

Give an example of a rational expression where the restricted value is 5 and -3

Answers vary

500

Solve the equation (x² +7x + 12)/6 = 7

x = 3 or x = -10