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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. 7.16 (page 648)

Simplify $\frac{\frac{y^{2} - 36}{2 y^{2} + 11 y - 6}}{\frac{2 y^{2} - 2 y - 60}{8 y - 4}}$ .

Short Answer

Expert verified

The simplest form of the given expression is $\frac{2}{(y + 5)} .$

Step by step solution

01

Step 1. Given information

The given expression is $\frac{\frac{y^{2} - 36}{2 y^{2} + 11 y - 6}}{\frac{2 y^{2} - 2 y - 60}{8 y - 4}}$

02

Step 2. Simplify

$\frac{\frac{y^{2} - 36}{2 y^{2} + 11 y - 6}}{\frac{2 y^{2} - 2 y - 60}{8 y - 4}} = \frac{y^{2} - 36}{2 y^{2} + 11 y - 6} 路 \frac{8 y - 4}{2 y^{2} - 2 y - 60} Convertdivisionintomultiplication = \frac{(y - 6) (y + 6)}{(2 y - 1) (y + 6)} 路 \frac{4 (2 y - 1)}{2 (y + 5) (y - 6)} Factorize = \frac{4 (2 y - 1) (y - 6) (y + 6)}{2 (y + 5) (y - 6) (2 y - 1) (y + 6)} Multiplynumeratoranddenominator = \frac{2}{(y + 5)} cancelcommonfactorsofnumeratoranddenominator$

Hence, The given expression is simplified as $\frac{2}{(y + 5)} .$

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Most popular questions from this chapter

In the following exercises, find the domain of each function.

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