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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 8.85 (page 903)

Add: $\frac{5 x}{x y - y^{2}} + \frac{2 x}{x^{2} - y^{2}}$

Short Answer

Expert verified

The addition of the rational expression is $\frac{x (5 x + 7 y)}{(x + y) (x - y) y}$

Step by step solution

01

Given information

The given rational expression $\frac{5 x}{x y - y^{2}} + \frac{2 x}{x^{2} - y^{2}}$ .

02

Simplify the rational expression

The LCD of the expression is $(x + y) (x - y) (y)$ $= \frac{5 x}{y (x - y)} + \frac{2 x}{(x + y) (x - y)} = \frac{5 x (x + y)}{y (x - y) (x + y)} + \frac{2 x y}{(x + y) (x - y) y} Add the rational expression \frac{= 5 x^{2} + 5 x y + 2 x y}{(x + y) (x - y) y} = \frac{5 x^{2} + 7 x y}{(x + y) (x - y) y} Simplify = \frac{x (5 x + 7 y)}{(x + y) (x - y) y}$

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