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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.57TI. (page 676)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{a}{b} + \frac{b}{a}}$

Short Answer

Expert verified

$\frac{a + b}{a^{2} + b^{2}}$

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

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

02

Step 2. Simplification of the complex rational expression.

The LCD of all the fractions in the numerator and the denominator is $a b$ .

Multiply the numerator and the denominator by that LCD:

$\frac{a b . (\frac{1}{a} + \frac{1}{b})}{a b . (\frac{a}{b} + \frac{b}{a})}$

Distribute:

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

Simplify:

$\frac{b + a}{a^{2} + b^{2}}$

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Most popular questions from this chapter

Joon drove 4 hours to his home, driving 208 miles on the interstate and 40 miles on the country roads. If he drove 15 mph faster on the interstate than on the country roads, what was his rate on the country roads?

Simplify the complex rational expression by writing it as division:

$\frac{\frac{3}{4} - \frac{1}{3}}{\frac{1}{8} + \frac{5}{6}}$

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In the following exercises, divide the rational expressions.

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