Precalculus Examples

$x + \frac{π}{3} = \frac{3 π}{4} + 2 n π$

Step 1

Subtract $\frac{π}{3}$ from both sides of the equation.

$x = \frac{3 π}{4} + 2 n π - \frac{π}{3}$

Step 2

To write $\frac{3 π}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 2 n π + \frac{3 π}{4} \cdot \frac{3}{3} - \frac{π}{3}$

Step 3

To write $- \frac{π}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = 2 n π + \frac{3 π}{4} \cdot \frac{3}{3} - \frac{π}{3} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3 π}{4}$ by $\frac{3}{3}$ .

$x = 2 n π + \frac{3 π \cdot 3}{4 \cdot 3} - \frac{π}{3} \cdot \frac{4}{4}$

Step 4.2

Multiply $4$ by $3$ .

$x = 2 n π + \frac{3 π \cdot 3}{12} - \frac{π}{3} \cdot \frac{4}{4}$

Step 4.3

Multiply $\frac{π}{3}$ by $\frac{4}{4}$ .

$x = 2 n π + \frac{3 π \cdot 3}{12} - \frac{π \cdot 4}{3 \cdot 4}$

Step 4.4

Multiply $3$ by $4$ .

$x = 2 n π + \frac{3 π \cdot 3}{12} - \frac{π \cdot 4}{12}$

Step 5

Combine the numerators over the common denominator.

$x = 2 n π + \frac{3 π \cdot 3 - π \cdot 4}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $3$ .

$x = 2 n π + \frac{9 π - π \cdot 4}{12}$

Step 6.2

Multiply $4$ by $- 1$ .

$x = 2 n π + \frac{9 π - 4 π}{12}$

Step 6.3

Subtract $4 π$ from $9 π$ .

$x = 2 n π + \frac{5 π}{12}$