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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. 7.14 (page 646)

Simplify $\frac{2 z^{2}}{z^{2} - 1} 梅 \frac{z^{3} - z^{2} + z}{z^{3} + 1}$

Short Answer

Expert verified

The simplest form of the given expression is

$\frac{2 z}{z - 1} .$

Step by step solution

01

Step 1. Given information

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

02

Step 2. Simplify

$\frac{2 z^{2}}{z^{2} - 1} 梅 \frac{z^{3} - z^{2} + z}{z^{3} + 1} = \frac{2 z^{2}}{z^{2} - 1} 脳 \frac{z^{3} + 1}{z^{3} - z^{2} + z} Convertdivisionintomultiplication = \frac{2 z 脳 z}{(z - 1) (z + 1)} 脳 \frac{(z + 1) (z^{2} - z + 1)}{z (z^{2} - z + 1)} Factorizenumeratoranddenominator = \frac{2 z}{(z - 1)} Removecommonfactorsofnumeratoranddenominator$

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

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