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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 8.97 (page 952)

Simplify: $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1}$

Short Answer

Expert verified

The simplification of the rational expression is $\frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)}$ .

Step by step solution

01

Given information

The given rational expression is $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1}$ .

02

The simplification of the rational expression

$\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{(v - 1) (v + 1)}$

The LCD of the expression is $(v + 1) (v - 1)$ .

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

$= \frac{v (v - 1)}{(v + 1) (v - 1)} + \frac{3 (v + 1)}{(v - 1) (v + 1)} - \frac{6}{(v + 1) (v - 1)} = \frac{v^{2} - v}{(v + 1) (v - 1)} + \frac{3 v + 3}{(v + 1) (v - 1)} - \frac{6}{(v + 1) (v - 1)} S i m p l i f y = \frac{v^{2} - v + 3 v + 3 - 6}{(v + 1) (v - 1)} = \frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)} (v^{2} + 2 v - 3) cannot factorized further . \frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)}$

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