Chapter 7: Q7.54TI. (page 674)

Simplify the complex rational expression by writing it as division:
$\frac{1 - \frac{3}{c + 4}}{\frac{1}{c + 4} + \frac{c}{3}}$

Short Answer

Expert verified

$\frac{3}{c + 3}$

Step by step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{1 - \frac{3}{c + 4}}{\frac{1}{c + 4} + \frac{c}{3}}$

Step 2. Simplification of the complex rational expression.

Find common denominators and simplify the numerator and the denominator:

$\frac{\frac{1 (c + 4)}{(c + 4)} - \frac{3}{c + 4}}{\frac{1.3}{3 (c + 4)} + \frac{c (c + 4)}{3 (c + 4)}} \frac{\frac{c + 4 - 3}{(c + 4)}}{\frac{3 + c (c + 4)}{3 (c + 4)}} \frac{\frac{(c + 1)}{(c + 4)}}{\frac{3 + c^{2} + 4 c}{3 (c + 4)}} \frac{\frac{(c + 1)}{(c + 4)}}{\frac{c^{2} + 4 c + 3}{3 (c + 4)}}$

Rewrite as a division problem:

$\frac{(c + 1)}{(c + 4)} \div \frac{c^{2} + 4 c + 3}{3 (c + 4)}$

Rewrite as a product of the first with the reciprocal of the second:

$\frac{(c + 1)}{(c + 4)} . \frac{3 (c + 4)}{c^{2} + 4 c + 3}$

Factor the numerator and the denominator terms (where applicable), cancel the common factors and simplify:

$\frac{(c + 1)}{(c + 4)} . \frac{3 (c + 4)}{(c + 3) (c + 1)} \frac{3}{c + 3}$

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Simplify the complex rational expression by writing it as division:
$\frac{1 - \frac{3}{c + 4}}{\frac{1}{c + 4} + \frac{c}{3}}$

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 writing it as division:1-3c+41c+4+c3

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

Applied Mathematics

Mechanics Maths

Decision Maths

Geometry

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by writing it as division:
$\frac{1 - \frac{3}{c + 4}}{\frac{1}{c + 4} + \frac{c}{3}}$