Simplify (2(x+3))/(x(x-1))*(4x(x+2))/(10(x+3))

$\frac{2 (x + 3)}{x (x - 1)} \cdot \frac{4 x (x + 2)}{10 (x + 3)}$

Step 1

Cancel the common factor of $2 (x + 3)$ .

Factor $2 (x + 3)$ out of $10 (x + 3)$ .

$\frac{2 (x + 3)}{x (x - 1)} \cdot \frac{4 x (x + 2)}{2 (x + 3) (5)}$

Cancel the common factor.

$\frac{2 (x + 3)}{x (x - 1)} \cdot \frac{4 x (x + 2)}{2 (x + 3) \cdot 5}$

Rewrite the expression.

$\frac{1}{x (x - 1)} \cdot \frac{4 x (x + 2)}{5}$

Step 2

Cancel the common factor of $x$ .

Factor $x$ out of $4 x (x + 2)$ .

$\frac{1}{x (x - 1)} \cdot \frac{x (4 (x + 2))}{5}$

Cancel the common factor.

$\frac{1}{x (x - 1)} \cdot \frac{x (4 (x + 2))}{5}$

Rewrite the expression.

$\frac{1}{x - 1} \cdot \frac{4 (x + 2)}{5}$

Step 3

Multiply $\frac{1}{x - 1}$ by $\frac{4 (x + 2)}{5}$ .

$\frac{4 (x + 2)}{(x - 1) \cdot 5}$

Step 4

Move $5$ to the left of $x - 1$ .

$\frac{4 (x + 2)}{5 (x - 1)}$