Simplify ((3q)/(q-5))/((24q^2)/(q^2-25))

$\frac{\frac{3 q}{q - 5}}{\frac{24 q^{2}}{q^{2} - 25}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 q}{q - 5} \cdot \frac{q^{2} - 25}{24 q^{2}}$

Simplify terms.

Cancel the common factor of $3 q$ .

Factor $3 q$ out of $24 q^{2}$ .

$\frac{3 q}{q - 5} \cdot \frac{q^{2} - 25}{3 q (8 q)}$

Cancel the common factor.

$\frac{3 q}{q - 5} \cdot \frac{q^{2} - 25}{3 q (8 q)}$

Rewrite the expression.

$\frac{1}{q - 5} \cdot \frac{q^{2} - 25}{8 q}$

Multiply $\frac{1}{q - 5}$ by $\frac{q^{2} - 25}{8 q}$ .

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

Simplify the numerator.

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

$\frac{q^{2} - 5^{2}}{(q - 5) \cdot 8 q}$

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

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

Cancel the common factor of $q - 5$ .

Cancel the common factor.

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

Rewrite the expression.

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