Chapter 11: Q. 166 (page 1069)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{4 + \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$

Short Answer

Expert verified

The simplified expression is $\frac{16}{b - 1}$ .

Step by step solution

Step 1. Given Information.

We have:

$\frac{4 + \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$

Step 2. Simplify the numerator.

The numerator is $4 + \frac{4}{b - 5}$ .

Apply fraction rule: $a + \frac{b}{c} = \frac{a c + b}{c}$

$= \frac{4 (b - 5) + 4}{b - 5} = \frac{4 b - 16}{b - 5}$

Step 3. Simplify the denominator.

The denominator is $\frac{1}{b - 5} + \frac{b}{4}$ .

The least common divisor is $4 (b - 5)$ .

Adjust the fractions based on the LCM:

$= \frac{4}{4 (b - 5)} + \frac{b (b - 5)}{4 (b - 5)} = \frac{4 + b (b - 5)}{4 (b - 5)} = \frac{4 + b^{2} - 5 b}{4 (b - 5)}$

Step 4. Substitute the simplified numerator and denominator into the original expression.

We have:

$\frac{4 + \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}} = \frac{\frac{4 b - 16}{b - 5}}{\frac{4 + b^{2} - 5 b}{4 (b - 5)}}$

Apply fraction rule: $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}$

localid="1662393230322" $= \frac{(4 b - 16) \cdot 4 (b - 5)}{(b - 5) (4 + b^{2} - 5 b)} = \frac{4 (b - 4) \cdot 4 (b - 5)}{(b - 5) (b - 1) (b - 4)} = \frac{16}{b - 1}$

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In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{4 + \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplify the numerator.

Step 3. Simplify the denominator.

Step 4. Substitute the simplified numerator and denominator into the original expression.

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In the following exercises, simplify each complex rational expression by writing it as division.4+ 4b-5 1b-5+b4

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplify the numerator.

Step 3. Simplify the denominator.

Step 4. Substitute the simplified numerator and denominator into the original expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Pure Maths

Decision Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{4 + \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$