Simplify (2x)/3-1/(3x^2)

$\frac{2 x}{3} - \frac{1}{3 x^{2}}$

Step 1

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

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

$\frac{2 x^{3} - 1}{3 x^{2}}$