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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. 7.17 (page 648)

Perform the indicated operations.
$\frac{4 m + 4}{3 m - 15} 路 \frac{m^{2} - 3 m - 10}{m^{2} - 4 m - 32} 梅 \frac{12 m - 36}{6 m - 48} .$

Short Answer

Expert verified

The simplest form of the given operations is

$\frac{2 (m + 1) (m + 2)}{3 (m + 4) (m - 3)} .$

Step by step solution

01

Step 1. Given information

The given expression is

$\frac{4 m + 4}{3 m - 15} 路 \frac{m^{2} - 3 m - 10}{m^{2} - 4 m - 32} 梅 \frac{12 m - 36}{6 m - 48}$

02

Step 2. Simplify the expression

$\frac{4 m + 4}{3 m - 15} 路 \frac{m^{2} - 3 m - 10}{m^{2} - 4 m - 32} 梅 \frac{12 m - 36}{6 m - 48} Given = \frac{4 m + 4}{3 m - 15} 路 \frac{m^{2} - 3 m - 10}{m^{2} - 4 m - 32} 路 \frac{6 m - 48}{12 m - 36} Writedivisionasmultiplication = \frac{4 (m + 1)}{3 (m - 5)} 路 \frac{(m - 5) (m + 2)}{(m - 8) (m + 4)} 路 \frac{6 (m - 8)}{12 (m - 3)} Factorizenumeratoranddenminator = \frac{2 路 2 路 6 (m + 1) (m - 5) (m + 2) (m - 8)}{2 路 3 路 6 (m - 5) (m - 8) (m + 4) (m - 3)} Multiplythefactors = \frac{2 (m + 1) (m + 2)}{3 (m + 4) (m - 3)} Removecommonfactorsofnumeratoranddenominator$

Hene, the simplified expression is $\frac{2 (m + 1) (m + 2)}{3 (m + 4) (m - 3)} .$

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