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

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $y$ .

Factor $y$ out of $y x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Factor $x$ out of $y x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{y x^{2} + x}{y x y + y}$

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

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

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

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

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

Factor $x$ out of $x^{1}$ .

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

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

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

Simplify the denominator.

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

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

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

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

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

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

Factor $y$ out of $y^{1}$ .

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

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

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

Cancel the common factor of $y x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{y}$

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

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