Chapter 8: Q 215 (page 954)

Subtract $\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$ .

Short Answer

Expert verified

The difference is $\frac{4 a^{2} + 25 a - 6}{(a + 3) (a + 6)}$ .

Step by step solution

Given Information

The Given expression is $\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$ .

Find the LCD of denominators.

Since there are no common denominators.

The LCD is $(a + 3) (a + 6)$ .

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{5 a (a + 6)}{(a + 3) (a + 6)} - \frac{(a + 2) (a + 3)}{(a + 3) (a + 6)}$

Simplify numerators.

$= \frac{5 a^{2} + 30 a}{(a + 3) (a + 6)} - \frac{a^{2} + 5 a + 6}{(a + 3) (a + 6)}$

Subtract and simplify the numerator.

Take common denominator.

$= \frac{5 a^{2} + 30 a - (a^{2} + 5 a + 6)}{(a + 3) (a + 6)}$

Simplify.

$= \frac{5 a^{2} + 30 a - a^{2} - 5 a - 6}{(a + 3) (a + 6)}$

$= \frac{4 a^{2} + 25 a - 6}{(a + 3) (a + 6)}$

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Subtract $\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$ .

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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Subtract5aa+3-a+2a+6.

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

Applied Mathematics

Discrete Mathematics

Pure Maths

Probability and Statistics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Subtract $\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$ .