Chapter 8: Q 217 (page 954)

Subtract $\frac{6 c}{c^{2} - 25} - \frac{3}{c + 5}$ .

Short Answer

Expert verified

The result is $\frac{3}{c - 5}$ .

Step by step solution

Given Information

The Given expression is $\frac{6 c}{c^{2} - 25} - \frac{3}{c + 5}$ .

Find the LCD of denominators.

Factor the denominators.

$c^{2} - 25 = (c + 5) (c - 5)$

$c + 5 = (c + 5)$

LCD $= (c + 5) (c - 5)$

Rewrite the expression in factored form.

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

Rewrite each fraction as an equivalent fraction with the LCD.

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

Simplify numerators.

$= \frac{6 c}{(c + 5) (c - 5)} - \frac{3 c - 15}{(c + 5) (c - 5)}$

Subtract and simplify the numerator.

Take common denominator.

$= \frac{6 c - (3 c - 15)}{(c + 5) (c - 5)}$

$= \frac{6 c - 3 c + 15}{(c + 5) (c - 5)}$

Simplify numerator.

$= \frac{3 c + 15}{(c + 5) (c - 5)}$

$= \frac{3 (c + 5)}{(c + 5) (c - 5)}$

$= \frac{3}{c - 5}$

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Subtract $\frac{6 c}{c^{2} - 25} - \frac{3}{c + 5}$ .

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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Subtract6cc2-25-3c+5.

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

Pure Maths

Mechanics Maths

Applied Mathematics

Logic and Functions

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Subtract $\frac{6 c}{c^{2} - 25} - \frac{3}{c + 5}$ .