Simplify 8/(5-c)-8/(5+c)

$\frac{8}{5 - c} - \frac{8}{5 + c}$

Step 1

To write $\frac{8}{5 - c}$ as a fraction with a common denominator, multiply by $\frac{5 + c}{5 + c}$ .

$\frac{8}{5 - c} \cdot \frac{5 + c}{5 + c} - \frac{8}{5 + c}$

Step 2

To write $- \frac{8}{5 + c}$ as a fraction with a common denominator, multiply by $\frac{5 - c}{5 - c}$ .

$\frac{8}{5 - c} \cdot \frac{5 + c}{5 + c} - \frac{8}{5 + c} \cdot \frac{5 - c}{5 - c}$

Step 3

Write each expression with a common denominator of $(5 - c) (5 + c)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{5 - c}$ by $\frac{5 + c}{5 + c}$ .

$\frac{8 (5 + c)}{(5 - c) (5 + c)} - \frac{8}{5 + c} \cdot \frac{5 - c}{5 - c}$

Multiply $\frac{8}{5 + c}$ by $\frac{5 - c}{5 - c}$ .

$\frac{8 (5 + c)}{(5 - c) (5 + c)} - \frac{8 (5 - c)}{(5 + c) (5 - c)}$

Reorder the factors of $(5 - c) (5 + c)$ .

$\frac{8 (5 + c)}{(5 + c) (5 - c)} - \frac{8 (5 - c)}{(5 + c) (5 - c)}$

Step 4

Combine the numerators over the common denominator.

$\frac{8 (5 + c) - 8 (5 - c)}{(5 + c) (5 - c)}$

Step 5

Simplify the numerator.

Factor $8$ out of $8 (5 + c) - 8 (5 - c)$ .

Factor $8$ out of $- 8 (5 - c)$ .

$\frac{8 (5 + c) + 8 (- (5 - c))}{(5 + c) (5 - c)}$

Factor $8$ out of $8 (5 + c) + 8 (- (5 - c))$ .

$\frac{8 (5 + c - (5 - c))}{(5 + c) (5 - c)}$

Apply the distributive property.

$\frac{8 (5 + c - 1 \cdot 5 - - c)}{(5 + c) (5 - c)}$

Multiply $- 1$ by $5$ .

$\frac{8 (5 + c - 5 - - c)}{(5 + c) (5 - c)}$

Multiply $- - c$ .

Multiply $- 1$ by $- 1$ .

$\frac{8 (5 + c - 5 + 1 c)}{(5 + c) (5 - c)}$

Multiply $c$ by $1$ .

$\frac{8 (5 + c - 5 + c)}{(5 + c) (5 - c)}$

Subtract $5$ from $5$ .

$\frac{8 (c + 0 + c)}{(5 + c) (5 - c)}$

Add $c$ and $0$ .

$\frac{8 (c + c)}{(5 + c) (5 - c)}$

Add $c$ and $c$ .

$\frac{8 \cdot 2 c}{(5 + c) (5 - c)}$

Multiply $8$ by $2$ .

$\frac{16 c}{(5 + c) (5 - c)}$