Simplify (x/(xy)-2)/(2xy-3/y)

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y$ .

Move the leading negative in $- \frac{3}{y}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify the denominator.

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

$\frac{1 - 2 y}{2 y^{2} x - 3}$