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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.486. (page 742)

Perform the indicated operation and simplify.
$\frac{2 y^{2}}{y^{2} - 1} 梅 \frac{y^{3} - y^{2} + y}{y^{3} - 1}$

Short Answer

Expert verified

The solution is $\frac{2 y (y^{2} + y + 1)}{(y + 1) (y^{2} - y + 1)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{2 y^{2}}{y^{2} - 1} 梅 \frac{y^{3} - y^{2} + y}{y^{3} - 1}$ .

02

Step 2. Simplify the rational expression.

$\frac{2 y^{2}}{y^{2} - 1} 梅 \frac{y^{3} - y^{2} + y}{y^{3} - 1} = \frac{2 y^{2}}{y^{2} - 1} 脳 \frac{y^{3} - 1}{y^{3} - y^{2} + y} \frac{2 y^{2}}{y^{2} - 1} 梅 \frac{y^{3} - y^{2} + y}{y^{3} - 1} = \frac{2 y^{2}}{(y + 1) (y - 1)} 脳 \frac{(y - 1) (y^{2} + y + 1)}{y (y^{2} - y + 1)} (R e m o v e t h e c o m m o n f a c t o r) \frac{2 y^{2}}{y^{2} - 1} 梅 \frac{y^{3} - y^{2} + y}{y^{3} - 1} = \frac{2 y (y^{2} + y + 1)}{(y + 1) (y^{2} - y + 1)}$

03

Step 3. Simplified answer.

Hence, the simplified expression is $\frac{2 y (y^{2} + y + 1)}{(y + 1) (y^{2} - y + 1)}$ .

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