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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 8.74 (page 939)

Subtract $\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$

Short Answer

Expert verified

The required expression is $\frac{3 n - 2}{n - 1}$

Step by step solution

01

Given information

The given expression is $\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$

02

Simplifying the expression

The denominators of two rational expressions are opposite, so multiply the second rational expression by $\frac{- 1}{- 1} :$

$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{(- 1) (n^{2} - 7 n - 1)}{(- 1) (1 - n^{2})}$

Simplifying the second expression, the two denominators become the same, combining the two expressions:

role="math" $\frac{2 n^{2} + 8 n - 1 + n^{2} - 7 n - 1}{n^{2} - 1}$

Combining the like terms:

$\frac{3 n^{2} + n - 2}{n^{2} - 1}$

Factorizing the numerator and denominator:

$\frac{(n + 1) (3 n - 2)}{(n - 1) (n + 1)}$

Cancel the common terms:

$\frac{3 n - 2}{n - 1}$

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