Precalculus Examples

$\frac{x}{2 x - 4} + \frac{1}{6}$

Step 1

Factor $2$ out of $2 x - 4$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{x}{2 (x) - 4} + \frac{1}{6}$

Step 1.2

Factor $2$ out of $- 4$ .

$\frac{x}{2 x + 2 \cdot - 2} + \frac{1}{6}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot - 2$ .

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

Step 2

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

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

Step 3

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

Step 4

Write each expression with a common denominator of $6 (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x}{2 (x - 2)}$ by $\frac{3}{3}$ .

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

Step 4.2

Multiply $3$ by $2$ .

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

Step 4.3

Multiply $\frac{1}{6}$ by $\frac{x - 2}{x - 2}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Add $x \cdot 3$ and $x$ .

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Step 6.1.1

Reorder $x$ and $3$ .

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

Step 6.1.2

Add $3 \cdot x$ and $x$ .

$\frac{4 \cdot x - 2}{6 (x - 2)}$

Step 6.2

Factor $2$ out of $4 \cdot x - 2$ .

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Step 6.2.1

Factor $2$ out of $4 \cdot x$ .

$\frac{2 (2 \cdot x) - 2}{6 (x - 2)}$

Step 6.2.2

Factor $2$ out of $- 2$ .

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

Step 6.2.3

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

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

$\frac{2 (2 x - 1)}{6 (x - 2)}$

Step 7

Cancel the common factors.

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Step 7.1

Factor $2$ out of $6 (x - 2)$ .

$\frac{2 (2 x - 1)}{2 (3 (x - 2))}$

Step 7.2

Cancel the common factor.

$\frac{2 (2 x - 1)}{2 (3 (x - 2))}$

Step 7.3

Rewrite the expression.

$\frac{2 x - 1}{3 (x - 2)}$