Simplify (5x(x-2))/((x+1)(x-6))*(x+1)/(10(x-2)(x-1))

$\frac{5 x (x - 2)}{(x + 1) (x - 6)} \cdot \frac{x + 1}{10 (x - 2) (x - 1)}$

Step 1

Cancel the common factor of $5 (x - 2)$ .

Factor $5 (x - 2)$ out of $5 x (x - 2)$ .

$\frac{5 (x - 2) (x)}{(x + 1) (x - 6)} \cdot \frac{x + 1}{10 (x - 2) (x - 1)}$

Factor $5 (x - 2)$ out of $10 (x - 2) (x - 1)$ .

$\frac{5 (x - 2) (x)}{(x + 1) (x - 6)} \cdot \frac{x + 1}{5 (x - 2) (2 (x - 1))}$

Cancel the common factor.

$\frac{5 (x - 2) x}{(x + 1) (x - 6)} \cdot \frac{x + 1}{5 (x - 2) (2 (x - 1))}$

Rewrite the expression.

$\frac{x}{(x + 1) (x - 6)} \cdot \frac{x + 1}{2 (x - 1)}$

Step 2

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{x}{(x + 1) (x - 6)} \cdot \frac{x + 1}{2 (x - 1)}$

Rewrite the expression.

$\frac{x}{x - 6} \cdot \frac{1}{2 (x - 1)}$

Step 3

Multiply $\frac{x}{x - 6}$ by $\frac{1}{2 (x - 1)}$ .

$\frac{x}{(x - 6) (2 (x - 1))}$

Step 4

Move $2$ to the left of $x - 6$ .

$\frac{x}{2 (x - 6) (x - 1)}$