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

Step 1. Given information.

The following complex rational expression is given:

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

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

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:1a+1bab+ba

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

Statistics

Mechanics Maths

Geometry

Decision Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

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