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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 392 (page 737)

Divide the rational expression $\frac{3 y^{2} - 12 y - 63}{4 y + 3} \div (6 y^{2} - 42 y)$

Short Answer

Expert verified

The value of the expression is $\frac{7}{2} .$

Step by step solution

01

Step 1. Given Information

Given that the expression is $\frac{3 y^{2} - 12 y - 63}{4 y + 3} \div (6 y^{2} - 42 y)$ and taken as $\frac{y^{2} - 8}{y^{2} - y - 2} .$

02

Step 2. Simplification

It can be simplified as,

$\frac{y^{2} - 8}{y^{2} - y - 2}, y = 1 = \frac{{(1)}^{2} - 8}{{(1)}^{2} - 1 - 2} = \frac{- 7}{- 2} = \frac{7}{2}$

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Most popular questions from this chapter

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

$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

Determine the values for which the rational expression is undefined.

$\frac{5 x^{2} y^{2}}{8 y}$

Simplify the complex rational expression by writing it as a division:

$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

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In the following exercises, Divide the rational expression

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

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