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

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

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

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

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

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

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Combine the numerators over the common denominator.

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