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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 117. (page 931)

Divide Rational Expressions: $\frac{\frac{2 a^{2} 鈥� 鈭� 鈥� a 鈥� 鈭� 鈥� 21}{5 a 鈥� + 鈥� 20}}{\frac{a^{2} 鈥� + 鈥� 7 a 鈥� + 鈥� 12}{a^{2} 鈥� + 鈥� 8 a 鈥� + 鈥� 16}}$

Short Answer

Expert verified

The required answer is $\frac{2 a - 7}{5}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{\frac{2 a^{2} - a - 21}{5 a + 20}}{\frac{a^{2} + 7 a + 12}{a^{2} + 8 a + 16}}$

02

Step 2. Simplify the expression.

$\frac{\frac{2 a^{2} - a - 21}{5 a + 20}}{\frac{a^{2} + 7 a + 12}{a^{2} + 8 a + 16}}$

Apply the fraction rule.

$= \frac{(2 a^{2} - a - 21) (a^{2} + 8 a + 16)}{(5 a + 20) (a^{2} + 7 a + 12)} = \frac{(a + 3) (2 a - 7) (a^{2} + 8 a + 16)}{(5 a + 20) (a + 3) (a + 4)} = \frac{(2 a - 7) (a^{2} + 8 a + 16)}{(5 a + 20) (a + 4)} = \frac{(2 a - 7) {(a + 4)}^{2}}{(5 a + 20) (a + 4)} = \frac{(2 a - 7) (a + 4) (a + 4)}{(5 a + 20) (a + 4)} = \frac{(2 a - 7) (a + 4)}{5 a + 20} = \frac{(2 a - 7) (a + 4)}{5 (a + 4)} = \frac{2 a - 7}{5}$

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