Divide ((3x+12)/(12x))÷((x+4)/(48x^3))

$\frac{3 x + 12}{12 x} \div \frac{x + 4}{48 x^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x + 12}{12 x} \cdot \frac{48 x^{3}}{x + 4}$

Step 2

Cancel the common factor of $12 x$ .

Factor $12 x$ out of $48 x^{3}$ .

$\frac{3 x + 12}{12 x} \cdot \frac{12 x (4 x^{2})}{x + 4}$

Cancel the common factor.

$\frac{3 x + 12}{12 x} \cdot \frac{12 x (4 x^{2})}{x + 4}$

Rewrite the expression.

$(3 x + 12) \frac{4 x^{2}}{x + 4}$

Step 3

Multiply $3 x + 12$ by $\frac{4 x^{2}}{x + 4}$ .

$\frac{(3 x + 12) (4 x^{2})}{x + 4}$

Step 4

Simplify the numerator.

Factor $3$ out of $3 x + 12$ .

Factor $3$ out of $3 x$ .

$\frac{(3 (x) + 12) \cdot 4 x^{2}}{x + 4}$

Factor $3$ out of $12$ .

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

Factor $3$ out of $3 x + 3 \cdot 4$ .

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

Multiply $4$ by $3$ .

$\frac{12 (x + 4) x^{2}}{x + 4}$

Step 5

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{12 (x + 4) x^{2}}{x + 4}$

Divide $12 x^{2}$ by $1$ .

$12 x^{2}$