Simplify (5/(x-2))÷(x/(x+1))

$\frac{5}{x - 2} \div \frac{x}{x + 1}$

To divide by a fraction, multiply by its reciprocal.

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

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

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

Reorder factors in $\frac{5 (x + 1)}{(x - 2) x}$ .

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