Precalculus Examples

$\frac{x^{2}}{3} - \frac{x}{18}$

Step 1

To write $\frac{x^{2}}{3}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x^{2}}{3} \cdot \frac{6}{6} - \frac{x}{18}$

Step 2

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{x^{2}}{3}$ by $\frac{6}{6}$ .

$\frac{x^{2} \cdot 6}{3 \cdot 6} - \frac{x}{18}$

Step 2.2

Multiply $3$ by $6$ .

$\frac{x^{2} \cdot 6}{18} - \frac{x}{18}$

Step 3

Combine the numerators over the common denominator.

$\frac{x^{2} \cdot 6 - x}{18}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $x^{2} \cdot 6 - x$ .

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Step 4.1.1

Factor $x$ out of $x^{2} \cdot 6$ .

$\frac{x (x \cdot 6) - x}{18}$

Step 4.1.2

Factor $x$ out of $- x$ .

$\frac{x (x \cdot 6) + x \cdot - 1}{18}$

Step 4.1.3

Factor $x$ out of $x (x \cdot 6) + x \cdot - 1$ .

$\frac{x (x \cdot 6 - 1)}{18}$

Step 4.2

Move $6$ to the left of $x$ .

$\frac{x (6 x - 1)}{18}$