Divide (5/(x-2))÷(x/(x+1))

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

Step 3

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $5$ by $1$ .

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

Step 6

Split the fraction $\frac{5 x + 5}{x (x - 2)}$ into two fractions.

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

Step 7

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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