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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. 50 (page 652)

In the following exercises, Divide the rational expression
$\frac{2 y^{2} - 10 y z - 48 z^{2}}{2 y - 1} 梅 (4 y^{2} - 32 y z)$

Short Answer

Expert verified

The simplified expression is $\frac{2 (y + 3 z)}{2 y (2 y - 1)}$

Step by step solution

01

Step 1. Given Information

$\frac{2 y^{2} - 10 y z - 48 z^{2}}{2 y - 1} 梅 (4 y^{2} - 32 y z) = \frac{2 y^{2} - 10 y z - 48 z^{2}}{2 y - 1} 脳 \frac{1}{(4 y^{2} - 32 y z)}$

02

Step 2. Factor the numerator and denominators

$= \frac{2 (y + 3 z) (y - 8 z)}{2 y - 1} 脳 \frac{1}{4 y (y - 8 z)} = \frac{2 (y + 3 z) (y - 8 z)}{4 y (2 y - 1) (y - 8 z)}$

03

Step 3. Remove the common factors

$= \frac{2 (y + 3 z)}{2 y (2 y - 1)}$

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Most popular questions from this chapter

For the following exercises, find $R (x) = f (x) . g (x)$ where $f (x) a n d g (x)$ are given.

localid="1644679377284" $f (x) = \frac{6 x^{2} - 12 x}{x^{2} + 7 x - 18} a n d g (x) = \frac{x^{2} - 81}{3 x^{2} - 27 x}$

In the following exercises, divide the rational expressions.

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