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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 432 (page 737)

In the following exercise, simplify $\frac{\frac{3}{a^{2}} - \frac{1}{b}}{\frac{1}{a} + \frac{1}{b^{2}}}$

Short Answer

Expert verified

The solution is $\frac{(3 b - a^{2}) b}{a (b^{2} + a)}$

Step by step solution

01

Step 1. Given Information

$\frac{(3 b - a^{2}) b}{a (b^{2} + a)}$

02

Step 2. Simplify

The LCD of all fractions in the complex rational expression is $(a^{2} b) (a b^{2})$

Multiply the numerator and denominator by the LCD.

$= \frac{(a^{2} b) (a b^{2}) (\frac{3}{a^{2}} - \frac{1}{b})}{(a^{2} b) (a b^{2}) (\frac{1}{a} + \frac{1}{b^{2}})} = \frac{((a^{2} b) (a b^{2}) \frac{3}{a^{2}} - (a^{2} b) (a b^{2}) \frac{1}{b})}{((a^{2} b) (a b^{2}) \frac{1}{a} + (a^{2} b) (a b^{2}) \frac{1}{b^{2}})} = \frac{3 a b^{3} - a^{3} b^{2}}{a^{2} b^{3} + a^{3} b} = \frac{(3 b - a^{2}) b}{a (b^{2} + a)}$

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