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

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

Step 1

Cancel the common factor of $x + 2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 3}{x - 4} \cdot \frac{1}{x}$

Step 3

Multiply $\frac{x - 3}{x - 4}$ by $\frac{1}{x}$ .

$\frac{x - 3}{(x - 4) x}$

Step 4

Reorder factors in $\frac{x - 3}{(x - 4) x}$ .

$\frac{x - 3}{x (x - 4)}$