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

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $y$ .

Factor $y$ out of $y x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Raise $x$ to the power of $1$ .

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

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Cancel the common factor of $x$ .

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

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

Factor $x$ out of $y x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Raise $y$ to the power of $1$ .

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

Raise $y$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Simplify the numerator.

Factor $x$ out of $x^{2} + y x \cdot 1$ .

Factor $x$ out of $x^{2}$ .

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

Factor $x$ out of $y x \cdot 1$ .

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

Factor $x$ out of $x \cdot x + x (y \cdot 1)$ .

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

Multiply $y$ by $1$ .

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

Simplify the denominator.

Factor $y$ out of $y x \cdot 1 - y^{2}$ .

Factor $y$ out of $y x \cdot 1$ .

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

Factor $y$ out of $- y^{2}$ .

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

Factor $y$ out of $y (x \cdot 1) + y (- y)$ .

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

Multiply $x$ by $1$ .

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

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

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