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

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

Step 1

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

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

Step 2

Write each expression with a common denominator of $6 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

$\frac{1 - 1 \cdot 2 (x^{2} x)}{6 x^{2}}$

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

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

$\frac{1 - 1 \cdot 2 (x^{2} x^{1})}{6 x^{2}}$

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

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

Add $2$ and $1$ .

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

Multiply $- 1$ by $2$ .

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