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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. 7.15 (page 647)

Simplify $\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}}$ .

Short Answer

Expert verified

The simplest form of the given expression is $\frac{(x + 2)}{4} .$

Step by step solution

01

Step 1. Given information

The given expression is $\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}} .$

02

Step 2. Simplify

$\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}} = \frac{3 x^{2} + 7 x + 2}{4 x + 24} 路 \frac{x^{2} + x - 30}{3 x^{2} - 14 x - 5} Convertdivistionintomultiplication = \frac{(x + 2) (3 x + 1)}{4 (x + 6)} 路 \frac{(x + 6) (x - 5)}{(x - 5) (3 x + 1)} Factorize = \frac{(x + 2) (3 x + 1) (x + 6) (x - 5)}{4 (x + 6) (x - 5) (3 x + 1)} Multiplynumeratoranddenominator = \frac{(x + 2)}{4} Cancelcommonfactorsofnumeratoranddenominator$

Hence, the given expresion is simplified as $\frac{(x + 2)}{4} .$

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Most popular questions from this chapter

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

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For the following exercises, perform the indicated operations.

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For the following exercises, perform the indicated operations.
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