Simplify (-2/x+5/y)/(3/y-2/x)

$\frac{\frac{- 2}{x} + \frac{5}{y}}{\frac{3}{y} - \frac{2}{x}}$

Step 1

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

Multiply $\frac{\frac{- 2}{x} + \frac{5}{y}}{\frac{3}{y} - \frac{2}{x}}$ by $\frac{x y}{x y}$ .

$\frac{x y}{x y} \cdot \frac{\frac{- 2}{x} + \frac{5}{y}}{\frac{3}{y} - \frac{2}{x}}$

Combine.

$\frac{x y (\frac{- 2}{x} + \frac{5}{y})}{x y (\frac{3}{y} - \frac{2}{x})}$

Step 2

Apply the distributive property.

$\frac{x y \frac{- 2}{x} + x y \frac{5}{y}}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Factor $x$ out of $x y$ .

$\frac{x (y) \frac{- 2}{x} + x y \frac{5}{y}}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Cancel the common factor.

$\frac{x y \frac{- 2}{x} + x y \frac{5}{y}}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Rewrite the expression.

$\frac{y \cdot - 2 + x y \frac{5}{y}}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Cancel the common factor of $y$ .

Factor $y$ out of $x y$ .

$\frac{y \cdot - 2 + y x \frac{5}{y}}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Cancel the common factor.

$\frac{y \cdot - 2 + y x \frac{5}{y}}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Rewrite the expression.

$\frac{y \cdot - 2 + x \cdot 5}{x y \frac{3}{y} + x y (- \frac{2}{x})}$

Cancel the common factor of $y$ .

Factor $y$ out of $x y$ .

$\frac{y \cdot - 2 + x \cdot 5}{y x \frac{3}{y} + x y (- \frac{2}{x})}$

Cancel the common factor.

$\frac{y \cdot - 2 + x \cdot 5}{y x \frac{3}{y} + x y (- \frac{2}{x})}$

Rewrite the expression.

$\frac{y \cdot - 2 + x \cdot 5}{x \cdot 3 + x y (- \frac{2}{x})}$

Cancel the common factor of $x$ .

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

$\frac{y \cdot - 2 + x \cdot 5}{x \cdot 3 + x y \frac{- 2}{x}}$

Factor $x$ out of $x y$ .

$\frac{y \cdot - 2 + x \cdot 5}{x \cdot 3 + x (y) \frac{- 2}{x}}$

Cancel the common factor.

$\frac{y \cdot - 2 + x \cdot 5}{x \cdot 3 + x y \frac{- 2}{x}}$

Rewrite the expression.

$\frac{y \cdot - 2 + x \cdot 5}{x \cdot 3 + y \cdot - 2}$

Step 4

Simplify the numerator.

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

$\frac{- 2 \cdot y + x \cdot 5}{x \cdot 3 + y \cdot - 2}$

Move $5$ to the left of $x$ .

$\frac{- 2 y + 5 x}{x \cdot 3 + y \cdot - 2}$

Step 5

Simplify the denominator.

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

$\frac{- 2 y + 5 x}{3 \cdot x + y \cdot - 2}$

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

$\frac{- 2 y + 5 x}{3 x - 2 y}$

Step 6

Simplify with factoring out.

Factor $- 1$ out of $- 2 y$ .

$\frac{- (2 y) + 5 x}{3 x - 2 y}$

Factor $- 1$ out of $5 x$ .

$\frac{- (2 y) - (- 5 x)}{3 x - 2 y}$

Factor $- 1$ out of $- (2 y) - (- 5 x)$ .

$\frac{- (2 y - 5 x)}{3 x - 2 y}$

Simplify the expression.

Rewrite $- (2 y - 5 x)$ as $- 1 (2 y - 5 x)$ .

$\frac{- 1 (2 y - 5 x)}{3 x - 2 y}$

Move the negative in front of the fraction.

$- \frac{2 y - 5 x}{3 x - 2 y}$

Simplify (-2/x+5/y)/(3/y-2/x)

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