Simplify 1/(x^2y^2)+1/(x^2y^3)

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

Step 1

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

$\frac{1}{x^{2} y^{2}} \cdot \frac{y}{y} + \frac{1}{x^{2} y^{3}}$

Step 2

Write each expression with a common denominator of $x^{2} y^{3}$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 3

Combine the numerators over the common denominator.

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