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: 54

Answer

$\frac{x^{2}-6x-4}{(x-1)(x+2)(x-4)}$

Work Step by Step

We form a common denominator, then add, factor, and simplify: $\displaystyle \frac{x}{x^{2}+x-2}-\frac{2}{x^{2}-5x+4}=\frac{x}{(x-1)(x+2)}+\frac{-2}{(x-1)(x-4)} =\frac{x(x-4)}{(x-1)(x+2)(x-4)}+\frac{-2(x+2)}{(x-1)(x+2)(x-4)}=\frac{x^{2}-4x-2x-4}{(x-1)(x+2)(x-4)}=\frac{x^{2}-6x-4}{(x-1)(x+2)(x-4)}$
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