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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 85. (page 930)

In the following exercises, multiply.
$\frac{x^{2} - 7 x}{x^{2} + 6 x + 9} 路 \frac{x + 3}{4 x}$

Short Answer

Expert verified

The required answer is $\frac{x - 7}{4 (x + 3)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{x^{2} - 7 x}{x^{2} + 6 x + 9} 路 \frac{x + 3}{4 x}$

02

Step 2. Simplify the expression.

$\frac{x^{2} - 7 x}{x^{2} + 6 x + 9} 路 \frac{x + 3}{4 x}$

Factor the numerator and denominator completely,

$\frac{x (x - 7)}{(x + 3) (x + 3)} 路 \frac{x + 3}{4 x}$

Multiply the numerators and denominators,

$\frac{x (x - 7) (x + 3)}{4 x (x + 3) (x + 3)}$

Simplify by dividing out common factors,

$\frac{x - 7}{4 (x + 3)}$

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