Precalculus Examples

$\frac{1}{5} + \frac{2}{x} - \frac{2}{3}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{5}$ by $\frac{3 x}{3 x}$ .

$\frac{1}{5} \cdot \frac{3 x}{3 x} + \frac{2}{x} - \frac{2}{3}$

Step 1.2

Multiply $\frac{1}{5}$ by $\frac{3 x}{3 x}$ .

$\frac{3 x}{5 (3 x)} + \frac{2}{x} - \frac{2}{3}$

Step 1.3

Multiply $\frac{2}{x}$ by $\frac{15}{15}$ .

$\frac{3 x}{5 (3 x)} + \frac{2}{x} \cdot \frac{15}{15} - \frac{2}{3}$

Step 1.4

Multiply $\frac{2}{x}$ by $\frac{15}{15}$ .

$\frac{3 x}{5 (3 x)} + \frac{2 \cdot 15}{x \cdot 15} - \frac{2}{3}$

Step 1.5

Multiply $\frac{2}{3}$ by $\frac{5 x}{5 x}$ .

$\frac{3 x}{5 (3 x)} + \frac{2 \cdot 15}{x \cdot 15} - (\frac{2}{3} \cdot \frac{5 x}{5 x})$

Step 1.6

Multiply $\frac{2}{3}$ by $\frac{5 x}{5 x}$ .

$\frac{3 x}{5 (3 x)} + \frac{2 \cdot 15}{x \cdot 15} - \frac{2 (5 x)}{3 (5 x)}$

Step 1.7

Reorder the factors of $5 (3 x)$ .

$\frac{3 x}{3 \cdot 5 x} + \frac{2 \cdot 15}{x \cdot 15} - \frac{2 (5 x)}{3 (5 x)}$

Step 1.8

Multiply $3$ by $5$ .

$\frac{3 x}{15 x} + \frac{2 \cdot 15}{x \cdot 15} - \frac{2 (5 x)}{3 (5 x)}$

Step 1.9

Reorder the factors of $x \cdot 15$ .

$\frac{3 x}{15 x} + \frac{2 \cdot 15}{15 x} - \frac{2 (5 x)}{3 (5 x)}$

Step 1.10

Reorder the factors of $3 (5 x)$ .

$\frac{3 x}{15 x} + \frac{2 \cdot 15}{15 x} - \frac{2 (5 x)}{3 \cdot 5 x}$

Step 1.11

Multiply $3$ by $5$ .

$\frac{3 x}{15 x} + \frac{2 \cdot 15}{15 x} - \frac{2 (5 x)}{15 x}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 x + 2 \cdot 15 - 2 (5 x)}{15 x}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $15$ .

$\frac{3 x + 30 - 2 (5 x)}{15 x}$

Step 3.2

Multiply $5$ by $- 2$ .

$\frac{3 x + 30 - 10 x}{15 x}$

Step 4

Simplify terms.

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Step 4.1

Subtract $10 x$ from $3 x$ .

$\frac{- 7 x + 30}{15 x}$

Step 4.2

Factor $- 1$ out of $- 7 x$ .

$\frac{- (7 x) + 30}{15 x}$

Step 4.3

Rewrite $30$ as $- 1 (- 30)$ .

$\frac{- (7 x) - 1 (- 30)}{15 x}$

Step 4.4

Factor $- 1$ out of $- (7 x) - 1 (- 30)$ .

$\frac{- (7 x - 30)}{15 x}$

Step 4.5

Simplify the expression.

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Step 4.5.1

Rewrite $- (7 x - 30)$ as $- 1 (7 x - 30)$ .

$\frac{- 1 (7 x - 30)}{15 x}$

Step 4.5.2

Move the negative in front of the fraction.

$- \frac{7 x - 30}{15 x}$