Simplify (1/(x-2))/(2+1/x)

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the denominator.

To write $2$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Combine the numerators over the common denominator.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

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

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