Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 54



Work Step by Step

$\frac{x}{x^{2}+x-2}-\frac{2}{x^{2}-5x+4}$ Factor the denominators: $=\frac{x}{(x-1)(x+2)}-\frac{2}{(x-1)(x-4)}$ Find the lowest common denominator (i.e. $(x-1)(x+2)(x-4)$) and adjust the fractions accordingly: $=\frac{x\times (x-4)}{(x-1)(x+2)(x-4)}-\frac{2\times (x+2)}{(x-1)(x+2)(x-4)}$ $=\frac{x^{2}-4x}{(x-1)(x+2)(x-4)}-\frac{2x+4}{(x-1)(x+2)(x-4)}$ Combine the fractions: $=\frac{x^{2}-4x-2x-4}{(x-1)(x+2)(x-4)}$ Simplify: $=\frac{x^{2}-6x-4}{(x-1)(x+2)(x-4)}$
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