Precalculus Examples

$\frac{x}{4} - \frac{3}{x}$

Step 1

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

$\frac{x}{4} \cdot \frac{x}{x} - \frac{3}{x}$

Step 2

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

$\frac{x}{4} \cdot \frac{x}{x} - \frac{3}{x} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{x \cdot x}{4 x} - \frac{3}{x} \cdot \frac{4}{4}$

Step 3.2

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

$\frac{x \cdot x}{4 x} - \frac{3 \cdot 4}{x \cdot 4}$

Step 3.3

Reorder the factors of $x \cdot 4$ .

$\frac{x \cdot x}{4 x} - \frac{3 \cdot 4}{4 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot x - 3 \cdot 4}{4 x}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $x$ by $x$ .

$\frac{x^{2} - 3 \cdot 4}{4 x}$

Step 5.2

Multiply $- 3$ by $4$ .

$\frac{x^{2} - 12}{4 x}$