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: 14

Answer

$\dfrac{3x-1}{x^{2}+5x-6}-\dfrac{2x-7}{x^{2}+5x-6}=\dfrac{1}{x-1}$

Work Step by Step

$\dfrac{3x-1}{x^{2}+5x-6}-\dfrac{2x-7}{x^{2}+5x-6}$ Evaluate the substraction of the two rational expressions: $\dfrac{3x-1}{x^{2}+5x-6}-\dfrac{2x-7}{x^{2}+5x-6}=\dfrac{(3x-1)-(2x-7)}{x^{2}+5x-6}=...$ $...=\dfrac{3x-1-2x+7}{x^{2}+5x-6}=\dfrac{x+6}{x^{2}+5x-6}=...$ Factor the denominator and simplify: $...=\dfrac{x+6}{(x+6)(x-1)}=\dfrac{1}{x-1}$
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