Simplify 1/(5x^3)+1/(15x)

$\frac{1}{5 x^{3}} + \frac{1}{15 x}$

To write $\frac{1}{5 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{5 x^{3}} \cdot \frac{3}{3} + \frac{1}{15 x}$

To write $\frac{1}{15 x}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{1}{5 x^{3}} \cdot \frac{3}{3} + \frac{1}{15 x} \cdot \frac{x^{2}}{x^{2}}$

Write each expression with a common denominator of $15 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5 x^{3}}$ by $\frac{3}{3}$ .

$\frac{3}{5 x^{3} \cdot 3} + \frac{1}{15 x} \cdot \frac{x^{2}}{x^{2}}$

Multiply $3$ by $5$ .

$\frac{3}{15 x^{3}} + \frac{1}{15 x} \cdot \frac{x^{2}}{x^{2}}$

Multiply $\frac{1}{15 x}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{3}{15 x^{3}} + \frac{x^{2}}{15 x \cdot x^{2}}$

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

Move $x^{2}$ .

$\frac{3}{15 x^{3}} + \frac{x^{2}}{15 (x^{2} x)}$

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

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

$\frac{3}{15 x^{3}} + \frac{x^{2}}{15 (x^{2} x^{1})}$

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

$\frac{3}{15 x^{3}} + \frac{x^{2}}{15 x^{2 + 1}}$

Add $2$ and $1$ .

$\frac{3}{15 x^{3}} + \frac{x^{2}}{15 x^{3}}$

Combine the numerators over the common denominator.

$\frac{3 + x^{2}}{15 x^{3}}$