Chapter 8: Q 230 (page 954)

Simplify $\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$ .

Short Answer

Expert verified

The result is $\frac{4 b + 1}{2 (b - 5)}$ .

Step by step solution

Given Information

The Given expression is $\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$ .

Find the LCD of denominators.

Factor the denominators.

$2 b^{2} - 10 b = 2 b (b - 5)$

LCD $= 2 b (b - 5)$

Rewrite the expression in factored form.

$\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b (b - 5)}$

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{2 b (2 b)}{2 b (b - 5)} + \frac{3 (b - 5)}{2 b (b - 5)} - \frac{2 b - 15}{2 b (b - 5)} = \frac{4 b^{2}}{2 b (b - 5)} + \frac{3 b - 15}{2 b (b - 5)} - \frac{2 b - 15}{2 b (b - 5)}$

Simplify.

Take common denominator.

$= \frac{4 b^{2} + 3 b - 15 - (2 b - 15)}{2 b (b - 5)} = \frac{4 b^{2} + 3 b - 15 - 2 b + 15}{2 b (b - 5)}$

Cancel common factors.

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

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Simplify $\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Simplify.

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Simplify2bb-5+32b-2b-152b2-10b.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify $\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$ .