Algebra Examples

$\frac{7}{15 x^{3}} + \frac{4}{3 x}$

Step 1

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

$\frac{7}{15 x^{3}} + \frac{4}{3 x} \cdot \frac{5 x^{2}}{5 x^{2}}$

Step 2

Write each expression with a common denominator of $15 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

$\frac{7}{15 x^{3}} + \frac{4 (5 x^{2})}{3 x (5 x^{2})}$

Step 2.2

Multiply $5$ by $3$ .

$\frac{7}{15 x^{3}} + \frac{4 (5 x^{2})}{15 x \cdot x^{2}}$

Step 2.3

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

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Step 2.3.1

Move $x^{2}$ .

$\frac{7}{15 x^{3}} + \frac{4 (5 x^{2})}{15 (x^{2} x)}$

Step 2.3.2

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

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Step 2.3.2.1

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

$\frac{7}{15 x^{3}} + \frac{4 (5 x^{2})}{15 (x^{2} x^{1})}$

Step 2.3.2.2

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

$\frac{7}{15 x^{3}} + \frac{4 (5 x^{2})}{15 x^{2 + 1}}$

Step 2.3.3

Add $2$ and $1$ .

$\frac{7}{15 x^{3}} + \frac{4 (5 x^{2})}{15 x^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 + 4 (5 x^{2})}{15 x^{3}}$

Step 4

Multiply $4$ by $5$ .

$\frac{7 + 20 x^{2}}{15 x^{3}}$