Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $4$ by $3$ .

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

Step 3.3

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

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

Step 3.4

Multiply $3$ by $4$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $4$ .

$\frac{8 + 3 x (3 x)}{12 x}$

Step 5.2

Rewrite using the commutative property of multiplication.

$\frac{8 + 3 \cdot 3 x \cdot x}{12 x}$

Step 5.3

Multiply $x$ by $x$ by adding the exponents.

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Step 5.3.1

Move $x$ .

$\frac{8 + 3 \cdot 3 (x \cdot x)}{12 x}$

Step 5.3.2

Multiply $x$ by $x$ .

$\frac{8 + 3 \cdot 3 x^{2}}{12 x}$

Step 5.4

Multiply $3$ by $3$ .

$\frac{8 + 9 x^{2}}{12 x}$