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: 64

Answer

$\frac{5}{(x-4)(x+3)(x+1)}$

Work Step by Step

We multiply by $(x-4)(x+1)$, distribute and simplify: $\displaystyle \frac{\frac{x-3}{x-4}-\frac{x+2}{x+1}}{x+3}=\frac{(x-3)(x+1)-(x+2)(x-4)}{(x-4)(x+3)(x+1)}=\frac{x^{2}-2x-3-(x^{2}-2x-8)}{(x-4)(x+3)(x+1)}=\frac{5}{(x-4)(x+3)(x+1)}$
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