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

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

Step 1

Simplify each term.

Cancel the common factor of $y$ and $y^{2}$ .

Factor $y$ out of $2 y$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $3 x$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

To write $\frac{2}{x y}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

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

Step 3

Write each expression with a common denominator of $x y^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{x y}$ by $\frac{y}{y}$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Step 4

Combine the numerators over the common denominator.

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