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

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

Step 1

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

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

Step 2

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

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

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

Reorder the factors of $y x^{2}$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $1$ .

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