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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 531 (page 1025)

In the following exercises, multiply.
$\frac{3 a^{2} + 21 a}{a^{2} + 6 a - 7} 路 \frac{a - 1}{a b}$

Short Answer

Expert verified

The answer is $\frac{3}{b} .$

Step by step solution

01

Step 1. Given Information.

The given expression is $\frac{3 a^{2} + 21 a}{a^{2} + 6 a - 7} 路 \frac{a - 1}{a b} .$

02

Step 2. Multiply.

Factor the numerator and denominator completely.

$\frac{3 a^{2} + 21 a}{a^{2} + 6 a - 7} 路 \frac{a - 1}{a b} = \frac{3 a (a + 7)}{(a - 1) (a + 7)} 路 \frac{a - 1}{a b}$

03

Step 3. Simplify.

Multiply the numerators and denominators.

$= \frac{3 a (a + 7) (a - 1)}{(a - 1) (a + 7) (a b)}$

Simplify by dividing out common factors.

$= \frac{3 路 a (a + 7) (a - 1)}{(a - 1) (a + 7) 路 a 路 b} = \frac{3}{b}$

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Most popular questions from this chapter

Efraim wants to start simplifying the complex fraction $\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{1}{b}}$ by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim鈥檚 plan.

Simplify

In the following exercises, use either method.

$\frac{\frac{v}{w} + \frac{1}{v}}{\frac{1}{v} 鈭� \frac{v}{w}}$

In the following exercises, simplify.

$\frac{\frac{5}{c^{2} + 5 c - 14}}{\frac{10}{c + 7}}$

In the following exercises, simplify.

$\frac{\frac{n}{m} + \frac{1}{n}}{\frac{1}{n} - \frac{n}{m}}$

In the following exercises, solve.

$1 - \frac{2}{m} = \frac{8}{m^{2}}$

See all solutions

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