Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set - Page 516: 53

Answer

$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}=\dfrac{23-5x}{(x-3)(x-2)}$

Work Step by Step

$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}$ Factor the denominator of the first fraction: $\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}=\dfrac{13}{(x-3)(x-2)}-\dfrac{5}{x-3}=...$ Evaluate the substraction of the two rational expressions and simplify: $...=\dfrac{13-5(x-2)}{(x-3)(x-2)}=\dfrac{13-5x+10}{(x-3)(x-2)}=\dfrac{-5x+23}{(x-3)(x-2)}=...$ $...=\dfrac{23-5x}{(x-3)(x-2)}$
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