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: 44

Answer

$\frac{x^{2}+3x+12}{(x-4)(x+6)}$

Work Step by Step

$\frac{x}{x-4}-\frac{3}{x+6}$ Find the lowest common denominator (i.e. $(x-4)(x+6)$) and adjust the fractions: $=\frac{x\times (x+6)}{(x-4)(x+6)}-\frac{3\times (x-4)}{(x-4)(x+6)}$ Expand any brackets: $=\frac{x^{2}+6x}{(x-4)(x+6)}-\frac{3x-12}{(x-4)(x+6)}$ Combine the fractions: $=\frac{x^{2}+6x-(3x-12)}{(x-4)(x+6)}$ Expand the negative sign: $=\frac{x^{2}+6x-3x+12}{(x-4)(x+6)}$ Collect like terms: $=\frac{x^{2}+3x+12}{(x-4)(x+6)}$
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