Simplify (3a^3-75a)/(a(a+5)(a+5))

$\frac{3 a^{3} - 75 a}{a (a + 5) (a + 5)}$

Simplify the numerator.

Factor $3 a$ out of $3 a^{3} - 75 a$ .

Factor $3 a$ out of $3 a^{3}$ .

$\frac{3 a (a^{2}) - 75 a}{a (a + 5) (a + 5)}$

Factor $3 a$ out of $- 75 a$ .

$\frac{3 a (a^{2}) + 3 a (- 25)}{a (a + 5) (a + 5)}$

Factor $3 a$ out of $3 a (a^{2}) + 3 a (- 25)$ .

$\frac{3 a (a^{2} - 25)}{a (a + 5) (a + 5)}$

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

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

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 $b = 5$ .

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

Simplify the denominator.

Raise $a + 5$ to the power of $1$ .

$\frac{3 a (a + 5) (a - 5)}{a ({(a + 5)}^{1} (a + 5))}$

Raise $a + 5$ to the power of $1$ .

$\frac{3 a (a + 5) (a - 5)}{a ({(a + 5)}^{1} {(a + 5)}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 a (a + 5) (a - 5)}{a {(a + 5)}^{1 + 1}}$

Add $1$ and $1$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a + 5$ and ${(a + 5)}^{2}$ .

Factor $a + 5$ out of $(3 (a + 5)) (a - 5)$ .

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

Cancel the common factors.

Factor $a + 5$ out of ${(a + 5)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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