Trigonometry Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

$\frac{x \cdot 5}{3 \cdot 5} - (\frac{1}{3} \cdot \frac{5}{5}) - \frac{1}{5}$

Step 1.4

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

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

Step 1.5

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

$\frac{x \cdot 5}{3 \cdot 5} - \frac{5}{3 \cdot 5} - (\frac{1}{5} \cdot \frac{3}{3})$

Step 1.6

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

$\frac{x \cdot 5}{3 \cdot 5} - \frac{5}{3 \cdot 5} - \frac{3}{5 \cdot 3}$

Step 1.7

Multiply $3$ by $5$ .

$\frac{x \cdot 5}{15} - \frac{5}{3 \cdot 5} - \frac{3}{5 \cdot 3}$

Step 1.8

Multiply $3$ by $5$ .

$\frac{x \cdot 5}{15} - \frac{5}{15} - \frac{3}{5 \cdot 3}$

Step 1.9

Reorder the factors of $5 \cdot 3$ .

$\frac{x \cdot 5}{15} - \frac{5}{15} - \frac{3}{3 \cdot 5}$

Step 1.10

Multiply $3$ by $5$ .

$\frac{x \cdot 5}{15} - \frac{5}{15} - \frac{3}{15}$

Step 2

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - 5 - 3}{15}$

Step 3

Move $5$ to the left of $x$ .

$\frac{5 x - 5 - 3}{15}$

Step 4

Subtract $3$ from $- 5$ .

$\frac{5 x - 8}{15}$