Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 8 - Rational Functions - 8-5 Adding and Subtracting Rational Expressions - Practice and Problem-Solving Exercises - Page 539: 29

Answer

$\dfrac{3}{x - 6}$

Work Step by Step

Do the subtraction in the denominator first. Find the least common denominator (LCD) of the two terms of the denominator and convert whole numbers to fractions: $\dfrac{\frac{3}{x - 4}}{\frac{x - 4}{x - 4} - \frac{2}{x - 4}}$ Perform the subtraction in the denominator: $=\dfrac{\frac{3}{x - 4}}{\frac{x - 4-2}{x - 4}}$ $=\dfrac{\frac{3}{x - 4}}{\frac{x - 6}{x - 4}}$ Rewrite this fraction as a division problem: $=\dfrac{3}{x - 4} \div \dfrac{x - 6}{x - 4}$ To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction: $=\dfrac{3}{x - 4} \cdot \dfrac{x - 4}{x - 6}$ Multiply numerator with numerator and denominator with denominator: $=\dfrac{3(x - 4)}{(x - 4)(x - 6)}$ Cancel common terms in the numerator and denominator: $=\dfrac{3}{x - 6}$
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