Simplify (4x-1)/(6x^3)+2/(3x^2)

$\frac{4 x - 1}{6 x^{3}} + \frac{2}{3 x^{2}}$

To write $\frac{2}{3 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{4 x - 1}{6 x^{3}} + \frac{2}{3 x^{2}} \cdot \frac{2 x}{2 x}$

Write each expression with a common denominator of $6 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3 x^{2}}$ by $\frac{2 x}{2 x}$ .

$\frac{4 x - 1}{6 x^{3}} + \frac{2 (2 x)}{3 x^{2} (2 x)}$

Multiply $2$ by $3$ .

$\frac{4 x - 1}{6 x^{3}} + \frac{2 (2 x)}{6 x^{2} x}$

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

$\frac{4 x - 1}{6 x^{3}} + \frac{2 (2 x)}{6 (x^{1} x^{2})}$

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

$\frac{4 x - 1}{6 x^{3}} + \frac{2 (2 x)}{6 x^{1 + 2}}$

Add $1$ and $2$ .

$\frac{4 x - 1}{6 x^{3}} + \frac{2 (2 x)}{6 x^{3}}$

Combine the numerators over the common denominator.

$\frac{4 x - 1 + 2 (2 x)}{6 x^{3}}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 x - 1 + 4 x}{6 x^{3}}$

Add $4 x$ and $4 x$ .

$\frac{8 x - 1}{6 x^{3}}$