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

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

Step 1

Multiply the numerator and denominator of the complex fraction by $x$ .

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply $x$ by $1$ .

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

Step 5

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

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