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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. 55 (page 653)

For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} 梅 \frac{5 m^{2} + 10 m}{2 m - 10}$

Short Answer

Expert verified

The simplified expression is $= \frac{4 (m + 8) (m + 7)}{3 (m - 4) (m + 2)}$

Step by step solution

01

Step 1. Given Information

$\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} 梅 \frac{5 m^{2} + 10 m}{2 m - 10}$

$= \frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} . \frac{2 m - 10}{5 m^{2} + 10 m}$

02

Step 2. Factor the numerator and denominator

$\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} . \frac{2 m - 10}{5 m^{2} + 10 m} = \frac{10 m (m + 8)}{3 (m - 3)} . \frac{(m + 7) (m - 3)}{(m - 4) (m - 5)} . \frac{2 (m - 5)}{5 m (m + 2)}$

03

Step 3. Multiply numerators and denominators

$= \frac{2 脳 10 m (m + 8) (m + 7) (m - 3) (m - 5)}{3 脳 5 m (m - 3) (m - 4) (m - 5) (m + 2)} .$

04

Step 4. Remove common factors and simplify

$= \frac{4 (m + 8) (m + 7)}{3 (m - 4) (m + 2)}$

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