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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 33. (page 918)

In the following exercises, simplify.
$\frac{a^{2} - a - 12}{a^{2} - 8 a + 16}$

Short Answer

Expert verified

The result is $\frac{a + 3}{a - 4}$ .

Step by step solution

01

Step 1. Given information.

Consider the given rational expression.

$\frac{a^{2} - a - 12}{a^{2} - 8 a + 16}$

02

Step 2. Calculation.

Factor the numerator and denominator and remove the common factor from the numerator and the denominator.

$\begin{array}{l} \frac{a^{2} - a - 12}{a^{2} - 8 a + 16} = \frac{a^{2} - 4 a + 3 a - 12}{a^{2} - 4 a - 4 a + 16} \\ = \frac{a (a - 4) + 3 (a - 4)}{a (a - 4) - 4 (a - 4)} \\ = \frac{(a - 4) (a + 3)}{(a - 4) (a - 4)} \\ = \frac{a + 3}{a - 4} \end{array}$

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