Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-2 Multiplying and Dividing Rational Expressions - Lesson Check: 4

Answer

$\frac{4x}{(x+7)(2x+3)}$

Work Step by Step

The reciprocal of a fraction $\frac{x}{y}$ is $\frac{y}{x}$. Dividing by a fraction is the same thing as multiplying by that fraction's reciprocal. First, we have to multiply together the numerators and the denominators: $\frac{8x^2-12x}{x+7}\div(4x^2-9) = \frac{8x^2-12x}{x+7}\div\frac{4x^2-9}{1} = \frac{8x^2-12x}{x+7}\cdot\frac{1}{4x^2-9} = \frac{8x^2-12x}{(x+7)(4x^2-9)}$ Then, we simplify: $\frac{(2x-3)(4x)}{(x+7)(2x-3)(2x+3)} = \frac{4x}{(x+7)(2x+3)}$
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