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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 118. (page 931)

Divide Rational Expressions: $\frac{\frac{3 b^{2} 鈥� + 鈥� 2 b 鈥� 鈭� 鈥� 8}{12 b 鈥� + 鈥� 18}}{\frac{3 b^{2} 鈥� + 鈥� 2 b 鈥� 鈭� 鈥� 8}{2 b^{2} 鈥� 鈭� 鈥� 7 b 鈥� 鈭� 鈥� 15}}$

Short Answer

Expert verified

The required answer is $\frac{b - 5}{6}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{\frac{3 b^{2} 鈥� + 鈥� 2 b 鈥� 鈭� 鈥� 8}{12 b 鈥� + 鈥� 18}}{\frac{3 b^{2} 鈥� + 鈥� 2 b 鈥� 鈭� 鈥� 8}{2 b^{2} 鈥� 鈭� 鈥� 7 b 鈥� 鈭� 鈥� 15}}$

02

Step 2. Simplify the expression.

$\frac{\frac{3 b^{2} 鈥� + 鈥� 2 b 鈥� 鈭� 鈥� 8}{12 b 鈥� + 鈥� 18}}{\frac{3 b^{2} 鈥� + 鈥� 2 b 鈥� 鈭� 鈥� 8}{2 b^{2} 鈥� 鈭� 鈥� 7 b 鈥� 鈭� 鈥� 15}}$

Apply the fraction rule.

$\frac{(3 b^{2} + 2 b - 8) (2 b^{2} - 7 b - 15)}{(12 b + 18) (3 b^{2} + 2 b - 8)} = \frac{2 b^{2} - 7 b - 15}{12 b + 18} = \frac{(2 b + 3) (b - 5)}{12 b + 18} = \frac{(2 b + 3) (b - 5)}{6 (2 b + 3)} = \frac{b - 5}{6}$

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