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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 8.51. (page 926)

Divide: $\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 梅 \frac{x^{2} - 4}{6}$ .

Short Answer

Expert verified

The required answer is $\frac{2 (x^{2} + 2 x + 4)}{(x + 2) (x^{2} - 2 x + 4)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 梅 \frac{x^{2} - 4}{6}$

02

Step 2. Simplify the expression.

$\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 梅 \frac{x^{2} - 4}{6}$

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

$\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 路 \frac{6}{x^{2} - 4}$

Factor the numerators and denominators and then multiply.

$\frac{(x - 2) (x^{2} + 2 x + 4)}{3 (x^{2} - 2 x + 4)} 路 \frac{6}{(x + 2) (x - 2)} \frac{2 路 3 (x - 2) (x^{2} + 2 x + 4)}{3 (x^{2} - 2 x + 4) (x + 2) (x - 2)}$

Simplify by dividing out common factors.

$\frac{2 (x^{2} + 2 x + 4)}{(x + 2) (x^{2} - 2 x + 4)}$

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