Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Mid-Chapter Check Point - Page 447: 9

Answer

$\frac{x^2-14x-16}{(x+6)(x-2)}$.

Work Step by Step

The given expression is $=\frac{2x-1}{x+6}-\frac{x+3}{x-2}$ LCM of all the denominators $=(x+6)(x-2)$ $=\frac{(x-2)}{(x-2)} \cdot \frac{2x-1}{x+6}-\frac{(x+6)}{(x+6)} \cdot \frac{x+3}{x-2}$ Simplify. $=\frac{(2x-1)(x-2)}{(x+6)(x-2)}- \frac{(x+6)(x+3)}{(x+6)(x-2)}$ $=\frac{(2x-1)(x-2)-(x+6)(x+3)}{(x+6)(x-2)}$ Use the distributive property. $=\frac{2x^2-x-4x+2-[x^2+3x+6x+18]}{x^2+6x-2x-12}$ Simplify. $=\frac{2x^2-x-4x+2-x^2-3x-6x-18}{x^2+6x-2x-12}$ $=\frac{x^2-14x-16}{x^2+4x-12}$ Factor the denominator $x^2+4x-12$. $=x^2+6x-2x-12$ $=(x^2+6x)+(-2x-12)$ $=x(x+6)-2(x+6)$ $=(x+6)(x-2)$ Substitute the factor. $=\frac{x^2-14x-16}{(x+6)(x-2)}$.
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