Algebra Examples

$\frac{2}{5 x^{4}} + \frac{x}{3}$

Step 1

To write $\frac{2}{5 x^{4}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2}{5 x^{4}} \cdot \frac{3}{3} + \frac{x}{3}$

Step 2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{5 x^{4}}{5 x^{4}}$ .

$\frac{2}{5 x^{4}} \cdot \frac{3}{3} + \frac{x}{3} \cdot \frac{5 x^{4}}{5 x^{4}}$

Step 3

Write each expression with a common denominator of $15 x^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{5 x^{4}}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 3}{5 x^{4} \cdot 3} + \frac{x}{3} \cdot \frac{5 x^{4}}{5 x^{4}}$

Step 3.2

Multiply $3$ by $5$ .

$\frac{2 \cdot 3}{15 x^{4}} + \frac{x}{3} \cdot \frac{5 x^{4}}{5 x^{4}}$

Step 3.3

Multiply $\frac{x}{3}$ by $\frac{5 x^{4}}{5 x^{4}}$ .

$\frac{2 \cdot 3}{15 x^{4}} + \frac{x (5 x^{4})}{3 (5 x^{4})}$

Step 3.4

Multiply $5$ by $3$ .

$\frac{2 \cdot 3}{15 x^{4}} + \frac{x (5 x^{4})}{15 x^{4}}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + x (5 x^{4})}{15 x^{4}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $3$ .

$\frac{6 + x (5 x^{4})}{15 x^{4}}$

Step 5.2

Rewrite using the commutative property of multiplication.

$\frac{6 + 5 x \cdot x^{4}}{15 x^{4}}$

Step 5.3

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 5.3.1

Move $x^{4}$ .

$\frac{6 + 5 (x^{4} x)}{15 x^{4}}$

Step 5.3.2

Multiply $x^{4}$ by $x$ .

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Step 5.3.2.1

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

$\frac{6 + 5 (x^{4} x^{1})}{15 x^{4}}$

Step 5.3.2.2

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

$\frac{6 + 5 x^{4 + 1}}{15 x^{4}}$

Step 5.3.3

Add $4$ and $1$ .

$\frac{6 + 5 x^{5}}{15 x^{4}}$