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

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

Step 1

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

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

Step 2

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

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

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Combine the numerators over the common denominator.

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