Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - Chapter 7 Review Problem Set: 3

Answer

$= \frac{3n+5}{n+2}$

Work Step by Step

$\frac{3n^{2}-n-10}{n^{2}-4}$ 1. Factor the numerator: $= \frac{3n^{2}-6n+5n-10}{n^{2}-4}$ $= \frac{3n(n-2)+5(n-2)}{n^{2}-4}$ $= \frac{(3n+5)(n-2)}{n^{2}-4}$ 2. Factor the denominator Whenever you only see a variable squared (without a coefficient) along with the subtraction of a perfect square, you know that it is a difference of two squares problem. Therefore, you use this shortcut to obtain: $= \frac{(3n+5)(n-2)}{(n-2)(n+2)}$ 3. Cancel out $n-2$ from the denominator and numerator $= \frac{(3n+5)}{(n+2)}$ $= \frac{3n+5}{n+2}$
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