Solve (3x+pi/4)-(3x-pi/6)/3

$$\frac { ( 3 x + \frac { \pi } { 4 } ) - ( 3 x - \frac { \pi } { 6 } ) } { 3 }$$

Evaluate

$$\frac{5\pi }{36}\approx 0.436332313$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{6}{6}.

$$\frac{3x+\frac{\pi }{4}-\left(\frac{6\times 3x}{6}-\frac{\pi }{6}\right)}{3}$$

Since \frac{6\times 3x}{6} and \frac{\pi }{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x+\frac{\pi }{4}-\frac{6\times 3x-\pi }{6}}{3}$$

Do the multiplications in 6\times 3x-\pi .

$$\frac{3x+\frac{\pi }{4}-\frac{18x-\pi }{6}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{4}{4}.

$$\frac{\frac{4\times 3x}{4}+\frac{\pi }{4}-\frac{18x-\pi }{6}}{3}$$

Since \frac{4\times 3x}{4} and \frac{\pi }{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4\times 3x+\pi }{4}-\frac{18x-\pi }{6}}{3}$$

Do the multiplications in 4\times 3x+\pi .

$$\frac{\frac{12x+\pi }{4}-\frac{18x-\pi }{6}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 6 is 12. Multiply \frac{12x+\pi }{4} times \frac{3}{3}. Multiply \frac{18x-\pi }{6} times \frac{2}{2}.

$$\frac{\frac{3\left(12x+\pi \right)}{12}-\frac{2\left(18x-\pi \right)}{12}}{3}$$

Since \frac{3\left(12x+\pi \right)}{12} and \frac{2\left(18x-\pi \right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3\left(12x+\pi \right)-2\left(18x-\pi \right)}{12}}{3}$$

Do the multiplications in 3\left(12x+\pi \right)-2\left(18x-\pi \right).

$$\frac{\frac{36x+3\pi -36x+2\pi }{12}}{3}$$

Combine like terms in 36x+3\pi -36x+2\pi .

$$\frac{\frac{5\pi }{12}}{3}$$

Express \frac{\frac{5\pi }{12}}{3} as a single fraction.

$$\frac{5\pi }{12\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{5\pi }{36}$$

Expand

$$\frac{5 \pi}{36} = 0.4363323129985824$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{6}{6}.

$$\frac{3x+\frac{\pi }{4}-\left(\frac{6\times 3x}{6}-\frac{\pi }{6}\right)}{3}$$

Since \frac{6\times 3x}{6} and \frac{\pi }{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x+\frac{\pi }{4}-\frac{6\times 3x-\pi }{6}}{3}$$

Do the multiplications in 6\times 3x-\pi .

$$\frac{3x+\frac{\pi }{4}-\frac{18x-\pi }{6}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{4}{4}.

$$\frac{\frac{4\times 3x}{4}+\frac{\pi }{4}-\frac{18x-\pi }{6}}{3}$$

Since \frac{4\times 3x}{4} and \frac{\pi }{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4\times 3x+\pi }{4}-\frac{18x-\pi }{6}}{3}$$

Do the multiplications in 4\times 3x+\pi .

$$\frac{\frac{12x+\pi }{4}-\frac{18x-\pi }{6}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 6 is 12. Multiply \frac{12x+\pi }{4} times \frac{3}{3}. Multiply \frac{18x-\pi }{6} times \frac{2}{2}.

$$\frac{\frac{3\left(12x+\pi \right)}{12}-\frac{2\left(18x-\pi \right)}{12}}{3}$$

Since \frac{3\left(12x+\pi \right)}{12} and \frac{2\left(18x-\pi \right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3\left(12x+\pi \right)-2\left(18x-\pi \right)}{12}}{3}$$

Do the multiplications in 3\left(12x+\pi \right)-2\left(18x-\pi \right).

$$\frac{\frac{36x+3\pi -36x+2\pi }{12}}{3}$$

Combine like terms in 36x+3\pi -36x+2\pi .

$$\frac{\frac{5\pi }{12}}{3}$$

Express \frac{\frac{5\pi }{12}}{3} as a single fraction.

$$\frac{5\pi }{12\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{5\pi }{36}$$