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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 8.89 (page 948)

Subtract: $\frac{y}{y + 4} - \frac{y - 2}{y - 5}$ .

Short Answer

Expert verified

The subtraction of the rational expression is $\frac{- 7 y + 8}{(y - 5) (y + 4)}$ .

Step by step solution

01

Given information

The given rational expression is $\frac{y}{y + 4} - \frac{y - 2}{y - 5}$ .

02

The simplification of the rational expression

$\frac{y}{y + 4} - \frac{y - 2}{y - 5}$

The LCD of the rational expression is $(y + 4) (y - 5)$ .

Change into equivalent fraction with the LCD.

$\frac{y (y - 5)}{(y + 4) (y - 5)} - \frac{(y - 2) (y + 4)}{(y - 5) (y + 4)}$

Simplify numerator

$\frac{y^{2} - 5 y}{(y + 4) (y - 5)} - \frac{y^{2} - 2 y + 4 y - 8}{(y - 5) (y + 4)}$

$\frac{y^{2} - 5 y - y^{2} - 2 y + 8}{(y - 5) (y + 4)} S i m p l i f y \frac{- 7 y + 8}{(y - 5) (y + 4)}$

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