Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator - Exercise Set: 13

Answer

$\dfrac{2x+3}{x^{2}-x-30}-\dfrac{x-2}{x^{2}-x-30}=\dfrac{1}{x-6}$

Work Step by Step

$\dfrac{2x+3}{x^{2}-x-30}-\dfrac{x-2}{x^{2}-x-30}$ Evaluate the substraction of the two rational expressions: $\dfrac{2x+3}{x^{2}-x-30}-\dfrac{x-2}{x^{2}-x-30}=\dfrac{2x+3-x+2}{x^{2}-x-30}=...$ $...=\dfrac{x+5}{x^{2}-x-30}=...$ Factor the denominator and then, simplify: $...=\dfrac{x+5}{(x-6)(x+5)}=\dfrac{1}{x-6}$
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