Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator - Exercise Set - Page 507: 31

Answer

$\displaystyle \frac{x}{2x-1}$

Work Step by Step

To subtract rational expressions with the same denominator, subtract numerators and place the difference over the common denominator. If possible, factor and simplify the result. --- Don't forget to place the second numerator in parentheses when subtracting. $\displaystyle \frac{3x+1}{4x-2}-\frac{x+1}{4x-2}= \displaystyle \frac{3x+1-(x+1)}{4x-2}$ $= \displaystyle \frac{3x+1-x-1}{4x-2}$ $= \displaystyle \frac{2x}{4x-2}$ $=\displaystyle \frac{2(x)}{2(2x-1)}$ ... reduce (divide the numerator and denominator with common factors) $=\displaystyle \frac{x}{2x-1}$
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