Algebra Examples

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

Step 1

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

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

Step 2

Write each expression with a common denominator of $x \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

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

Step 2.2

Move $2$ to the left of $x$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $3$ by $2$ .

$\frac{6 + 3}{2 x} + \frac{1}{2}$

Step 4.2

Add $6$ and $3$ .

$\frac{9}{2 x} + \frac{1}{2}$

Step 5

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

$\frac{9}{2 x} + \frac{1}{2} \cdot \frac{x}{x}$

Step 6

Multiply $\frac{1}{2}$ by $\frac{x}{x}$ .

$\frac{9}{2 x} + \frac{x}{2 x}$

Step 7

Combine the numerators over the common denominator.

$\frac{9 + x}{2 x}$