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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 8: Q 8.53. (page 927)

Divide: $\frac{2 x^{2} - 14 x - 16}{4} \div (x^{2} + 2 x + 1)$ .

Short Answer

Expert verified

The required answer is $\frac{x - 8}{2 (x + 1)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{2 x^{2} - 14 x - 16}{4} \div (x^{2} + 2 x + 1)$

02

Step 2. Simplify the expression.

$\frac{2 x^{2} - 14 x - 16}{4} \div (x^{2} + 2 x + 1)$

Rewrite the division as the product of the first rational expression and the reciprocal of the second.

$\frac{2 x^{2} - 14 x - 16}{4} \cdot \frac{1}{(x^{2} + 2 x + 1)}$

Factor the numerators and denominators and then multiply.

$\frac{2 (x + 1) (x - 8)}{4} \cdot \frac{1}{(x + 1) (x + 1)} \frac{2 (x + 1) (x - 8)}{4 (x + 1) (x + 1)}$

Simplify by dividing out common factors.

$\frac{x - 8}{2 (x + 1)}$

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