Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $6 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $2$ .

$\frac{5 \cdot 3}{6 x^{3}} + \frac{4}{3 x^{2}} \cdot \frac{2 x}{2 x}$

Step 3.3

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

$\frac{5 \cdot 3}{6 x^{3}} + \frac{4 (2 x)}{3 x^{2} (2 x)}$

Step 3.4

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6 x^{3}} + \frac{4 (2 x)}{6 x^{2} x}$

Step 3.5

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

$\frac{5 \cdot 3}{6 x^{3}} + \frac{4 (2 x)}{6 (x^{1} x^{2})}$

Step 3.6

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

$\frac{5 \cdot 3}{6 x^{3}} + \frac{4 (2 x)}{6 x^{1 + 2}}$

Step 3.7

Add $1$ and $2$ .

$\frac{5 \cdot 3}{6 x^{3}} + \frac{4 (2 x)}{6 x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 4 (2 x)}{6 x^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $3$ .

$\frac{15 + 4 \cdot 2 x}{6 x^{3}}$

Step 5.2

Multiply $4$ by $2$ .

$\frac{15 + 8 x}{6 x^{3}}$