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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply $x$ by $1$ .

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

Step 5

Simplify the denominator.

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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