Simplify ((16m^2)/(m^2+5))/((4m)/(3m^2+15))

$\frac{\frac{16 m^{2}}{m^{2} + 5}}{\frac{4 m}{3 m^{2} + 15}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{16 m^{2}}{m^{2} + 5} \cdot \frac{3 m^{2} + 15}{4 m}$

Simplify terms.

Cancel the common factor of $4 m$ .

Factor $4 m$ out of $16 m^{2}$ .

$\frac{4 m (4 m)}{m^{2} + 5} \cdot \frac{3 m^{2} + 15}{4 m}$

Cancel the common factor.

$\frac{4 m (4 m)}{m^{2} + 5} \cdot \frac{3 m^{2} + 15}{4 m}$

Rewrite the expression.

$\frac{4 m}{m^{2} + 5} (3 m^{2} + 15)$

Multiply $\frac{4 m}{m^{2} + 5}$ by $3 m^{2} + 15$ .

$\frac{4 m (3 m^{2} + 15)}{m^{2} + 5}$

Simplify the numerator.

Factor $3$ out of $3 m^{2} + 15$ .

Factor $3$ out of $3 m^{2}$ .

$\frac{4 m (3 (m^{2}) + 15)}{m^{2} + 5}$

Factor $3$ out of $15$ .

$\frac{4 m (3 m^{2} + 3 \cdot 5)}{m^{2} + 5}$

Factor $3$ out of $3 m^{2} + 3 \cdot 5$ .

$\frac{4 m (3 (m^{2} + 5))}{m^{2} + 5}$

$\frac{4 m \cdot 3 (m^{2} + 5)}{m^{2} + 5}$

Multiply $3$ by $4$ .

$\frac{12 m (m^{2} + 5)}{m^{2} + 5}$

Cancel the common factor of $m^{2} + 5$ .

Cancel the common factor.

$\frac{12 m (m^{2} + 5)}{m^{2} + 5}$

Divide $12 m$ by $1$ .

$12 m$