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 - Page 43: 52



Work Step by Step

$\frac{x}{x^{2}-4}+\frac{1}{x-2}$ Factorise $x^{2}-4$ and replace in fraction: $=\frac{x}{(x+2)(x-2)}+\frac{1}{x-2}$ Find the lowest common denominator (i.e. $(x+2)(x-2)$) and adjust accordingly: $=\frac{x}{(x+2)(x-2)}+\frac{1\times (x+2)}{(x-2)\times (x+2)}$ $=\frac{x}{(x+2)(x-2)}+\frac{x+2}{(x-2)(x+2)}$ Combine the fractions: $=\frac{x+x+2}{(x+2)(x-2)}$ Simplify: $=\frac{2x+2}{(x+2)(x-2)}$
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