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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 163 (page 941)

Subtract $\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$

Short Answer

Expert verified

The required expression is $\frac{4 b - 3}{b - 7}$

Step by step solution

01

Given information

The given expression is $\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$

02

Simplifying the expression

The denominators are opposite, multiply the second expression with $\frac{- 1}{- 1} :$

$\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} + \frac{2 b^{2} - 5 b - 8}{b^{2} - 49}$

Combining the numerator:

$\frac{4 b^{2} + 25 b - 21}{b^{2} - 49}$

Factorizing numerator and denominator:

$\frac{(b + 7) (4 b - 3)}{(b + 7) (b - 7)}$

Cancelling the common factor:

$\frac{4 b - 3}{b - 7}$

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