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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 8.94 (page 950)

Subtract $\frac{- 2 y - 2}{y^{2} 梅 2 y - 8} - \frac{y - 1}{2 - y}$

Short Answer

Expert verified

The simplification of the expression is $\frac{y^{2} - 7 y + 2}{(y - 4) (y + 2)}$ .

Step by step solution

01

Given information

The given rational expression is $\frac{- 2 y - 2}{y^{2} + 2 y - 8} - \frac{y - 1}{2 - y}$ .

02

The simplification of the rational expression

$\frac{- 2 y - 2}{y^{2} + 2 y - 8} - \frac{y - 1}{2 - y}$

Factor the numerator

$\frac{- 2 y - 2}{y^{2} + 2 y - 4 y - 8} - \frac{y - 1}{2 - y} \frac{- 2 y - 2}{y (y + 2) - 4 (y + 2)} - \frac{y - 1}{2 - y} \frac{- 2 y - 2}{(y - 4) (y + 2)} - \frac{y - 1}{2 - y}$

Since $(y - 2) a n d (2 - y)$ are opposites ,we will multiply the second rational expression by $\frac{- 1}{- 1}$ .

$= \frac{- 2 y - 2}{(y - 4) (y + 2)} - \frac{(- 1) y - 1}{(- 1) (2 - y)}$

The LCD of the expression is $(y - 4) (y - 2)$ .

Rewrite each rational expression as an equivalent rational expression with the LCD.

$= \frac{- 2 y - 2}{(y - 4) (y + 2)} - \frac{- y + 1 (y - 4)}{(y - 4) (y - 2)} = \frac{- 2 y - 2}{(y - 4) (y + 2)} - \frac{- y^{2} + 4 y + y - 4}{(y - 4) (y + 2)} S i m p l i f y = \frac{- 2 y - 2 + y^{2} - 4 y - y + 4}{(y - 4) (y + 2)} = \frac{y^{2} - 7 y + 2}{(y - 4) (y + 2)}$

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