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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. 8.109 (page 962)

Simplify: $\frac{\frac{1}{a} + \frac{1}{b}}{\frac{a}{b} + \frac{b}{a}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{b + a}{a^{2} + b^{2}}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{a}{b} + \frac{b}{a}}$

02

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is $a b$ . Clear the fractions by multiplying the numerator and denominator by that LCD.

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

03

Step 3. Conclusion.

The simplified form of the given expression is $\frac{b + a}{a^{2} + b^{2}}$ .

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