Trigonometry Examples

$\frac{2 π + 4}{6 π - 6} - \frac{3 π}{6 π}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2 π + 4$ and $6 π - 6$ .

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Step 1.1.1

Factor $2$ out of $2 π$ .

$\frac{2 (π) + 4}{6 π - 6} - \frac{3 π}{6 π}$

Step 1.1.2

Factor $2$ out of $4$ .

$\frac{2 π + 2 \cdot 2}{6 π - 6} - \frac{3 π}{6 π}$

Step 1.1.3

Factor $2$ out of $2 π + 2 \cdot 2$ .

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

Step 1.1.4

Cancel the common factors.

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Step 1.1.4.1

Factor $2$ out of $6 π$ .

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

Step 1.1.4.2

Factor $2$ out of $- 6$ .

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

Step 1.1.4.3

Factor $2$ out of $2 (3 π) + 2 (- 3)$ .

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

Step 1.1.4.4

Cancel the common factor.

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

Step 1.1.4.5

Rewrite the expression.

$\frac{π + 2}{3 π - 3} - \frac{3 π}{6 π}$

Step 1.2

Cancel the common factor of $3$ and $6$ .

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Step 1.2.1

Factor $3$ out of $3 π$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $6 π$ .

$\frac{π + 2}{3 π - 3} - \frac{3 (π)}{3 (2 π)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{π + 2}{3 π - 3} - \frac{3 π}{3 (2 π)}$

Step 1.2.2.3

Rewrite the expression.

$\frac{π + 2}{3 π - 3} - \frac{π}{2 π}$

Step 1.3

Cancel the common factor of $π$ .

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Step 1.3.1

Cancel the common factor.

$\frac{π + 2}{3 π - 3} - \frac{π}{2 π}$

Step 1.3.2

Rewrite the expression.

$\frac{π + 2}{3 π - 3} - \frac{1}{2}$

Step 2

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

$\frac{π + 2}{3 π - 3} \cdot \frac{2}{2} - \frac{1}{2}$

Step 3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3 π - 3}{3 π - 3}$ .

$\frac{π + 2}{3 π - 3} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{3 π - 3}{3 π - 3}$

Step 4

Write each expression with a common denominator of $(3 π - 3) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π + 2}{3 π - 3}$ by $\frac{2}{2}$ .

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

Step 4.2

Multiply $\frac{1}{2}$ by $\frac{3 π - 3}{3 π - 3}$ .

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

Step 4.3

Reorder the factors of $(3 π - 3) \cdot 2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Move $2$ to the left of $π$ .

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

Step 6.3

Multiply $2$ by $2$ .

$\frac{2 \cdot π + 4 - (3 π - 3)}{2 (3 π - 3)}$

Step 6.4

Apply the distributive property.

$\frac{2 π + 4 - (3 π) - - 3}{2 (3 π - 3)}$

Step 6.5

Multiply $3$ by $- 1$ .

$\frac{2 π + 4 - 3 π - - 3}{2 (3 π - 3)}$

Step 6.6

Multiply $- 1$ by $- 3$ .

$\frac{2 π + 4 - 3 π + 3}{2 (3 π - 3)}$

Step 6.7

Subtract $3 π$ from $2 π$ .

$\frac{4 - π + 3}{2 (3 π - 3)}$

Step 6.8

Add $4$ and $3$ .

$\frac{7 - π}{2 (3 π - 3)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7 - π}{2 (3 π - 3)}$

Decimal Form:

$0.30027554 \dots$