Algebra Examples

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

Step 1

To write $\frac{1}{3 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Multiply $\frac{1}{3 x}$ by $\frac{2}{2}$ .

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

Step 2.2

Multiply $2$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Add $2$ and $1$ .

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

Step 5

Cancel the common factor of $3$ and $6$ .

Tap for more steps...

Step 5.1

Factor $3$ out of $3$ .

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

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $3$ out of $6 x$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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

Step 7

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

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

Step 8

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

Tap for more steps...

Step 8.1

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

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

Step 8.2

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

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

Step 8.3

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

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

Step 8.4

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

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

Step 8.5

Add $1$ and $1$ .

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

Step 8.6

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

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

Step 8.7

Reorder the factors of $x^{2} \cdot 2$ .

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

Step 9

Combine the numerators over the common denominator.

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