Algebra Examples

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

Step 1

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3 x^{2}}{3 x^{2}}$ .

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

Step 2

To write $\frac{1}{3 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3

Write each expression with a common denominator of $12 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x}{4}$ by $\frac{3 x^{2}}{3 x^{2}}$ .

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

Step 3.2

Multiply $3$ by $4$ .

$\frac{x (3 x^{2})}{12 x^{2}} + \frac{1}{3 x^{2}} \cdot \frac{4}{4}$

Step 3.3

Multiply $\frac{1}{3 x^{2}}$ by $\frac{4}{4}$ .

$\frac{x (3 x^{2})}{12 x^{2}} + \frac{4}{3 x^{2} \cdot 4}$

Step 3.4

Multiply $4$ by $3$ .

$\frac{x (3 x^{2})}{12 x^{2}} + \frac{4}{12 x^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{x (3 x^{2}) + 4}{12 x^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{3 x \cdot x^{2} + 4}{12 x^{2}}$

Step 5.2

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

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Step 5.2.1

Move $x^{2}$ .

$\frac{3 (x^{2} x) + 4}{12 x^{2}}$

Step 5.2.2

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

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Step 5.2.2.1

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

$\frac{3 (x^{2} x^{1}) + 4}{12 x^{2}}$

Step 5.2.2.2

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

$\frac{3 x^{2 + 1} + 4}{12 x^{2}}$

Step 5.2.3

Add $2$ and $1$ .

$\frac{3 x^{3} + 4}{12 x^{2}}$