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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. 330 (page 982)

In the following exercises, solve.
$\frac{y - 3}{y^{2} - 4 y - 5} = \frac{1}{y + 1} + \frac{8}{y - 5}$

Short Answer

Expert verified

The solution is $y = - \frac{3}{4}$

Step by step solution

01

Step 1. Given information

The given rational expression is $\frac{y - 3}{y^{2} - 4 y - 5} = \frac{1}{y + 1} + \frac{8}{y - 5}$

02

Step 2. Eliminating fractions

The least common denominator is $(y + 1) (y - 5)$

Multiply the equation by LCD,

$(y + 1) (y - 5) 脳 \frac{y - 3}{y^{2} - 4 y - 5} = [\frac{1}{y + 1} + \frac{8}{y - 5}] (y + 1) (y - 5) y^{2} - 4 y - 5 脳 \frac{y - 3}{y^{2} - 4 y - 5} = y - 5 + 8 (y + 1) y - 3 = y - 5 + 8 y + 8 y - 3 = 9 y + 3 8 y = - 6 y = - \frac{6}{8} y = - \frac{3}{4}$

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