Simplify 1/y-1/(x^2y^2)

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

Step 1

To write $\frac{1}{y}$ as a fraction with a common denominator, multiply by $\frac{y x^{2}}{y x^{2}}$ .

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

Step 2

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

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Step 3

Combine the numerators over the common denominator.

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