Chapter 7: Q. 7.64 (page 678)

Simplify the complex rational expression by using the LCD:
$\frac{1 + \frac{1}{x - 1}}{\frac{3}{x + 1}}$

Short Answer

Expert verified

The simplified expression is $\frac{x (x + 1)}{3 (x - 1)}$ .

Step by step solution

Step 1. Given Information.

We have:

$\frac{1 + \frac{1}{x - 1}}{\frac{3}{x + 1}}$

Step 2. Multiply the numerator and denominator by the LCD.

The least common divisor (LCD) is $(x - 1) (x + 1)$ .

Multiply the numerator and denominator by $(x - 1) (x + 1) :$

$= \frac{(x - 1) (x + 1) (1 + \frac{1}{x - 1})}{(x - 1) (x + 1) (\frac{3}{x + 1})}$

Step 3. Simplify the expression

Distribute in the denominator and simplify:

$= \frac{1 (x - 1) (x + 1) + (x - 1) (x + 1) \frac{1}{x - 1}}{(x - 1) (x + 1) \times \frac{3}{x + 1}} = \frac{1 (x - 1) (x + 1) + (x + 1)}{3 (x - 1)} = \frac{(x + 1) (x - 1 + 1)}{3 (x - 1)} = \frac{x (x + 1)}{3 (x - 1)}$

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Simplify the complex rational expression by using the LCD:
$\frac{1 + \frac{1}{x - 1}}{\frac{3}{x + 1}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Multiply the numerator and denominator by the LCD.

Step 3. Simplify the expression

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Simplify the complex rational expression by using the LCD:1+1x-13x+1

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Multiply the numerator and denominator by the LCD.

Step 3. Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by using the LCD:
$\frac{1 + \frac{1}{x - 1}}{\frac{3}{x + 1}}$