College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 56

Answer

$\frac{-2x-1}{(x-3)(x+2)}$

Work Step by Step

We form a common denominator, then add, factor, and simplify: $\displaystyle \frac{x}{x^{2}-x-6}-\frac{1}{x+2}-\frac{2}{x-3}=\frac{x}{(x-3)(x+2)}+\frac{-1}{x+2}+\frac{-2}{x-3} =\frac{x}{(x-3)(x+2)}+\frac{-1(x-3)}{(x-3)(x+2)}+\frac{-2(x+2)}{(x-3)(x+2)}=\frac{x-x+3-2x-4}{(x-3)(x+2)}=\frac{-2x-1}{(x-3)(x+2)}$
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