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

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

Multiply $y$ by $1$ .

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

Multiply $y$ by $1$ .

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