Simplify (2x+5)/(x^2-64)-2/(x+8)

$\frac{2 x + 5}{x^{2} - 64} - \frac{2}{x + 8}$

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$\frac{2 x + 5}{x^{2} - 8^{2}} - \frac{2}{x + 8}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 8$ .

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

To write $- \frac{2}{x + 8}$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

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

Simplify terms.

Multiply $\frac{2}{x + 8}$ by $\frac{x - 8}{x - 8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 2$ by $- 8$ .

$\frac{2 x + 5 - 2 x + 16}{(x + 8) (x - 8)}$

Subtract $2 x$ from $2 x$ .

$\frac{0 + 5 + 16}{(x + 8) (x - 8)}$

Add $0$ and $5$ .

$\frac{5 + 16}{(x + 8) (x - 8)}$

Add $5$ and $16$ .

$\frac{21}{(x + 8) (x - 8)}$