Simplify (1+1/y)/(1-1/y)

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

$\frac{y \cdot 1 + y \frac{1}{y}}{y \cdot 1 + y (- \frac{1}{y})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y \cdot 1 + y \frac{1}{y}}{y \cdot 1 + y (- \frac{1}{y})}$

Rewrite the expression.

$\frac{y \cdot 1 + 1}{y \cdot 1 + y (- \frac{1}{y})}$

Cancel the common factor of $y$ .

Move the leading negative in $- \frac{1}{y}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify.

Multiply $y$ by $1$ .

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

Multiply $y$ by $1$ .

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