Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{2}$ and $x^{3}$ .

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

Step 1.2

Combine $\frac{1}{3}$ and $x^{3}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $3$ .

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

Step 4.3

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

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

Step 4.4

Multiply $3$ by $2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Reorder $x^{3}$ and $2$ .

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

Step 7

Add $3 \cdot x^{3}$ and $2 \cdot x^{3}$ .

$\frac{5 x^{3}}{6} - \frac{1}{2}$