Divide ((45x^4)/(3x+6))÷75x^3

$\frac{45 x^{4}}{3 x + 6} \div 75 x^{3}$

Rewrite the division as a fraction.

$\frac{\frac{45 x^{4}}{3 x + 6}}{75 x^{3}}$

Cancel the common factor of $45$ and $3 x + 6$ .

Factor $3$ out of $45 x^{4}$ .

$\frac{\frac{3 (15 x^{4})}{3 x + 6}}{75 x^{3}}$

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{\frac{3 (15 x^{4})}{3 (x) + 6}}{75 x^{3}}$

Factor $3$ out of $6$ .

$\frac{\frac{3 (15 x^{4})}{3 x + 3 \cdot 2}}{75 x^{3}}$

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{\frac{3 (15 x^{4})}{3 (x + 2)}}{75 x^{3}}$

Cancel the common factor.

$\frac{\frac{3 (15 x^{4})}{3 (x + 2)}}{75 x^{3}}$

Rewrite the expression.

$\frac{\frac{15 x^{4}}{x + 2}}{75 x^{3}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{15 x^{4}}{x + 2} \cdot \frac{1}{75 x^{3}}$

Cancel the common factor of $15 x^{3}$ .

Factor $15 x^{3}$ out of $15 x^{4}$ .

$\frac{15 x^{3} (x)}{x + 2} \cdot \frac{1}{75 x^{3}}$

Factor $15 x^{3}$ out of $75 x^{3}$ .

$\frac{15 x^{3} (x)}{x + 2} \cdot \frac{1}{15 x^{3} (5)}$

Cancel the common factor.

$\frac{15 x^{3} x}{x + 2} \cdot \frac{1}{15 x^{3} \cdot 5}$

Rewrite the expression.

$\frac{x}{x + 2} \cdot \frac{1}{5}$

Multiply $\frac{x}{x + 2}$ by $\frac{1}{5}$ .

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

Move $5$ to the left of $x + 2$ .

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