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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 91. (page 930)

In the following exercises, multiply.
$\frac{35 d - 7 d^{2}}{d^{2} + 7 d} 路 \frac{d^{2} + 12 d + 35}{d^{2} - 25}$

Short Answer

Expert verified

The required answer is $- 7$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{35 d - 7 d^{2}}{d^{2} + 7 d} 路 \frac{d^{2} + 12 d + 35}{d^{2} - 25}$

02

Step 2. Simplify the expression.

$\frac{35 d - 7 d^{2}}{d^{2} + 7 d} 路 \frac{d^{2} + 12 d + 35}{d^{2} - 25}$

Factor the numerator and denominator completely,

$\frac{7 d (5 - d)}{d (d + 7)} 路 \frac{(d + 7) (d + 5)}{(d - 5) (d + 5)}$

Multiply the numerators and denominators,

$- \frac{7 d (d - 5) (d + 7) (d + 5)}{d (d + 7) (d - 5) (d + 5)}$

Simplify by dividing out common factors,

$- 7$

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