Simplify (3/y+7/x)/(1/y-2/x)

$\frac{\frac{3}{y} + \frac{7}{x}}{\frac{1}{y} - \frac{2}{x}}$

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

Multiply $\frac{\frac{3}{y} + \frac{7}{x}}{\frac{1}{y} - \frac{2}{x}}$ by $\frac{y x}{y x}$ .

$\frac{y x}{y x} \cdot \frac{\frac{3}{y} + \frac{7}{x}}{\frac{1}{y} - \frac{2}{x}}$

Combine.

$\frac{y x (\frac{3}{y} + \frac{7}{x})}{y x (\frac{1}{y} - \frac{2}{x})}$

Apply the distributive property.

$\frac{y x \frac{3}{y} + y x \frac{7}{x}}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Simplify by cancelling.

Cancel the common factor of $y$ .

Factor $y$ out of $y x$ .

$\frac{y (x) \frac{3}{y} + y x \frac{7}{x}}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Cancel the common factor.

$\frac{y x \frac{3}{y} + y x \frac{7}{x}}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Rewrite the expression.

$\frac{x \cdot 3 + y x \frac{7}{x}}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Cancel the common factor of $x$ .

Factor $x$ out of $y x$ .

$\frac{x \cdot 3 + x y \frac{7}{x}}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Cancel the common factor.

$\frac{x \cdot 3 + x y \frac{7}{x}}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Rewrite the expression.

$\frac{x \cdot 3 + y \cdot 7}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Cancel the common factor of $y$ .

Factor $y$ out of $y x$ .

$\frac{x \cdot 3 + y \cdot 7}{y (x) \frac{1}{y} + y x (- \frac{2}{x})}$

Cancel the common factor.

$\frac{x \cdot 3 + y \cdot 7}{y x \frac{1}{y} + y x (- \frac{2}{x})}$

Rewrite the expression.

$\frac{x \cdot 3 + y \cdot 7}{x + y x (- \frac{2}{x})}$

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{2}{x}$ into the numerator.

$\frac{x \cdot 3 + y \cdot 7}{x + y x \frac{- 2}{x}}$

Factor $x$ out of $y x$ .

$\frac{x \cdot 3 + y \cdot 7}{x + x y \frac{- 2}{x}}$

Cancel the common factor.

$\frac{x \cdot 3 + y \cdot 7}{x + x y \frac{- 2}{x}}$

Rewrite the expression.

$\frac{x \cdot 3 + y \cdot 7}{x + y \cdot - 2}$

Simplify the numerator.

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + y \cdot 7}{x + y \cdot - 2}$

Move $7$ to the left of $y$ .

$\frac{3 x + 7 y}{x + y \cdot - 2}$

Move $- 2$ to the left of $y$ .

$\frac{3 x + 7 y}{x - 2 y}$

Simplify (3/y+7/x)/(1/y-2/x)

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