Simplify (a^2+8a-5a-40)/(a^2-25)

$\frac{a^{2} + 8 a - 5 a - 40}{a^{2} - 25}$

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(a^{2} + 8 a) - 5 a - 40}{a^{2} - 25}$

Factor out the greatest common factor (GCF) from each group.

$\frac{a (a + 8) - 5 (a + 8)}{a^{2} - 25}$

Factor the polynomial by factoring out the greatest common factor, $a + 8$ .

$\frac{(a + 8) (a - 5)}{a^{2} - 25}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = 5$ .

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

Cancel the common factor of $a - 5$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{a + 8}{a + 5}$