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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.51TI. (page 673)

Simplify the complex rational expression by writing it as division:
$\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}$

Short Answer

Expert verified

$\frac{y + x}{y - x}$

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}$

02

Step 2. Simplification of the complex rational expression.

Find a common denominator and add the fractions present at the numerator:

$\frac{\frac{1 . y}{x . y} + \frac{1 . x}{y . x}}{\frac{1}{x} - \frac{1}{y}}$

Find a common denominator and subtract the terms present at the denominator:

$\frac{\frac{1 . y}{x . y} + \frac{1 . x}{y . x}}{\frac{1 . y}{x . y} - \frac{1 . x}{y . x}}$

Simplify:

$\frac{\frac{y}{x y} + \frac{x}{x y}}{\frac{y}{x y} - \frac{x}{x y}} \frac{\frac{y + x}{x y}}{\frac{y - x}{x y}}$

Write as a division problem:

$\frac{y + x}{x y} 梅 \frac{y - x}{x y}$

Write as the product of the first and the reciprocal of the second:

$\frac{y + x}{x y} . \frac{x y}{y - x}$

Cancel out the common factors from the numerator and the denominator and simplify:

$\frac{y + x}{y - x}$

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