Chapter 8: Q 216 (page 954)

Subtract $\frac{3 b}{b - 2} - \frac{b - 6}{b - 8}$ .

Short Answer

Expert verified

The difference is $\frac{2 (b^{2} - 8 b - 6)}{(b - 2) (b - 8)}$ .

Step by step solution

Given Information

The Given expression is $\frac{3 b}{b - 2} - \frac{b - 6}{b - 8}$ .

Find the LCD of denominators.

Since there are no common denominators.

The LCD is $(b - 2) (b - 8)$ .

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{3 b (b - 8)}{(b - 2) (b - 8)} - \frac{(b - 6) (b - 2)}{(b - 2) (b - 8)}$

Simplify numerator.

$= \frac{3 b^{2} - 24 b}{(b - 2) (b - 8)} - \frac{b^{2} - 2 b - 6 b + 12}{(b - 2) (b - 8)}$

Subtract and simplify the numerator.

Take common denominator.

$= \frac{3 b^{2} - 24 b - (b^{2} - 8 b + 12)}{(b - 2) (b - 8)}$

$= \frac{3 b^{2} - 24 b - b^{2} + 8 b - 12}{(b - 2) (b - 8)}$

Simplify numerator.

$= \frac{2 b^{2} - 16 b - 12}{(b - 2) (b - 8)}$

$= \frac{2 (b^{2} - 8 b - 6)}{(b - 2) (b - 8)}$

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Subtract $\frac{3 b}{b - 2} - \frac{b - 6}{b - 8}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract and simplify the numerator.

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Subtract3bb-2-b-6b-8.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract and simplify the numerator.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Subtract $\frac{3 b}{b - 2} - \frac{b - 6}{b - 8}$ .