Precalculus Examples

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

Step 1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine $6$ and $\frac{2 x}{2 x}$ .

$\frac{3}{2 x} + \frac{6 (2 x)}{2 x}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 + 6 (2 x)}{2 x}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $3$ out of $3 + 6 \cdot 2 x$ .

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Step 3.1.1

Factor $3$ out of $3$ .

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

Step 3.1.2

Factor $3$ out of $6 \cdot 2 x$ .

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

Step 3.1.3

Factor $3$ out of $3 (1) + 3 (2 \cdot 2 x)$ .

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

Step 3.2

Multiply $2$ by $2$ .

$\frac{3 (1 + 4 x)}{2 x}$