Chapter 7: Q. 7.58 (page 676)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{1}{x^{2}} - \frac{1}{y^{2}}}{\frac{1}{x} + \frac{1}{y}}$

Short Answer

Expert verified

The simplified answer is $\frac{y - x}{x y}$

Step by step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{1}{x^{2}} - \frac{1}{y^{2}}}{\frac{1}{x} + \frac{1}{y}}$

Step 2. Simplification of the complex rational expression.

The LCD of all the fractions in the numerator and the denominator is $x^{2} y^{2}$ .

Multiply both the numerator and the denominator by the LCD:

$\frac{x^{2} y^{2} . (\frac{1}{x^{2}} - \frac{1}{y^{2}})}{x^{2} y^{2} . (\frac{1}{x} + \frac{1}{y})}$

Distribute:

$\frac{x^{2} y^{2} . \frac{1}{x^{2}} - x^{2} y^{2} . \frac{1}{y^{2}}}{x^{2} y^{2} . \frac{1}{x} + x^{2} y^{2} . \frac{1}{y}}$

Simplify:

$\frac{y^{2} - x^{2}}{x y^{2} + x^{2} y}$

Factor the numerator and the denominator, c cancel the common terms and simplify:

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

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Simplify the complex rational expression by using the LCD:
$\frac{\frac{1}{x^{2}} - \frac{1}{y^{2}}}{\frac{1}{x} + \frac{1}{y}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the complex rational expression.

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Simplify the complex rational expression by using the LCD:1x2-1y21x+1y

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the complex rational expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Probability and Statistics

Calculus

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by using the LCD:
$\frac{\frac{1}{x^{2}} - \frac{1}{y^{2}}}{\frac{1}{x} + \frac{1}{y}}$