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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. 58 (page 653)

For the following exercises, perform the indicated operations.
$\frac{6 q + 3}{9 q^{2} - 9 q} 梅 \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6}$

Short Answer

Expert verified

The solution is $\frac{2 (q + 5)}{9 (q + 11)}$

Step by step solution

01

Step 1. Given Information

$\frac{6 q + 3}{9 q^{2} - 9 q} 梅 \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6} = \frac{6 q + 3}{9 q^{2} - 9 q} . \frac{q^{2} + 4 q - 5}{q^{2} + 14 q + 33} . \frac{4 q^{2} + 12 q}{12 q + 6}$

02

Step 2. Factors the numerator and denominator

$\frac{6 q + 3}{9 q^{2} - 9 q} . \frac{q^{2} + 4 q - 5}{q^{2} + 14 q + 33} . \frac{4 q^{2} + 12 q}{12 q + 6} = \frac{3 (2 q + 1)}{9 q (q - 1)} . \frac{(q + 5) (q - 1)}{(q + 11) (q + 3)} . \frac{4 q (q + 3)}{6 (2 q + 1)}$

03

Step 3. Multiply the numerators and denominators

$\frac{3 脳 4 q (2 q + 1) (q + 5) (q - 1) (q + 3)}{9 q 脳 6 (2 q + 1) (q + 11) (q + 3) (q - 1)} .$

04

Step 4. Simplify by dividing out common factors

$\frac{2 (q + 5)}{9 (q + 11)}$

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Most popular questions from this chapter

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child鈥檚 weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?

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For the following exercises, perform the indicated operations.
$\frac{12 p^{2} + 3 p}{p + 3} 梅 \frac{p^{2} + 2 p - 63}{p^{2} - p - 12} . \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Simplify the rational expression $\frac{12 p - 240}{5 p - 100} .$

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