Simplify (8x^3)/(x+4)*(x^2+4x)/(12x^2)

$\frac{8 x^{3}}{x + 4} \cdot \frac{x^{2} + 4 x}{12 x^{2}}$

Step 1

Factor $x$ out of $x^{2} + 4 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{8 x^{3}}{x + 4} \cdot \frac{x \cdot x + 4 x}{12 x^{2}}$

Factor $x$ out of $4 x$ .

$\frac{8 x^{3}}{x + 4} \cdot \frac{x \cdot x + x \cdot 4}{12 x^{2}}$

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

$\frac{8 x^{3}}{x + 4} \cdot \frac{x (x + 4)}{12 x^{2}}$

Step 2

Cancel the common factor of $4 x^{2}$ .

Factor $4 x^{2}$ out of $8 x^{3}$ .

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

Factor $4 x^{2}$ out of $12 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $x (x + 4)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x \cdot \frac{x}{3}$

Step 4

Combine $2$ and $\frac{x}{3}$ .

$x \cdot \frac{2 x}{3}$

Step 5

Combine $x$ and $\frac{2 x}{3}$ .

$\frac{x (2 x)}{3}$

Step 6

Raise $x$ to the power of $1$ .

$\frac{2 (x^{1} x)}{3}$

Step 7

Raise $x$ to the power of $1$ .

$\frac{2 (x^{1} x^{1})}{3}$

Step 8

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

$\frac{2 x^{1 + 1}}{3}$

Step 9

Add $1$ and $1$ .

$\frac{2 x^{2}}{3}$