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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 114. (page 931)

Divide Rational Expressions: $\frac{x^{2} 鈥� + 鈥� 3 x 鈥� 鈭� 鈥� 10}{4 x} 梅 (2 x^{2} + 鈥� 20 x 鈥� + 鈥� 50)$

Short Answer

Expert verified

The required answer is $\frac{x - 2}{8 x (x + 5)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{x^{2} 鈥� + 鈥� 3 x 鈥� 鈭� 鈥� 10}{4 x} 梅 (2 x^{2} + 鈥� 20 x 鈥� + 鈥� 50)$ .

02

Step 2. Simplify the expression.

$\frac{x^{2} 鈥� + 鈥� 3 x 鈥� 鈭� 鈥� 10}{4 x} 梅 (2 x^{2} + 鈥� 20 x 鈥� + 鈥� 50) = \frac{\frac{x^{2} + 3 x - 10}{4 x}}{2 x^{2} + 20 x + 50}$

Apply the fraction rule.

$\frac{x^{2} + 3 x - 10}{4 x (2 x^{2} + 20 x + 50)} = \frac{(x - 2) (x + 5)}{4 x (2 x^{2} + 20 x + 50)} = \frac{(x - 2) (x + 5)}{4 x 路鈥� 2 {(x + 5)}^{2}}$

03

Apply exponent law.

$\frac{(x - 2) (x + 5)}{4 x 路鈥� 2 (x + 5) (x + 5)} = \frac{x - 2}{4 x 路鈥� 2 (x + 5)} = \frac{x - 2}{8 x (x + 5)}$

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Most popular questions from this chapter

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