Solve S/frac{S/3{V}+S/3/2V+S/3/V}

$$\frac { S } { \frac { S / 3 } { V } + \frac { S / 3 } { 2 V } + \frac { S / 3 } { V } }$$

Evaluate

$$\frac{6V}{5}$$

Short Solution Steps

Express \frac{\frac{S}{3}}{V} as a single fraction.

$$\frac{S}{\frac{S}{3V}+\frac{\frac{S}{3}}{2V}+\frac{\frac{S}{3}}{V}}$$

Express \frac{\frac{S}{3}}{2V} as a single fraction.

$$\frac{S}{\frac{S}{3V}+\frac{S}{3\times 2V}+\frac{\frac{S}{3}}{V}}$$

Multiply 3 and 2 to get 6.

$$\frac{S}{\frac{S}{3V}+\frac{S}{6V}+\frac{\frac{S}{3}}{V}}$$

Express \frac{\frac{S}{3}}{V} as a single fraction.

$$\frac{S}{\frac{S}{3V}+\frac{S}{6V}+\frac{S}{3V}}$$

Combine \frac{S}{3V} and \frac{S}{3V} to get 2\times \frac{S}{3V}.

$$\frac{S}{2\times \frac{S}{3V}+\frac{S}{6V}}$$

Express 2\times \frac{S}{3V} as a single fraction.

$$\frac{S}{\frac{2S}{3V}+\frac{S}{6V}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3V and 6V is 6V. Multiply \frac{2S}{3V} times \frac{2}{2}.

$$\frac{S}{\frac{2\times 2S}{6V}+\frac{S}{6V}}$$

Since \frac{2\times 2S}{6V} and \frac{S}{6V} have the same denominator, add them by adding their numerators.

$$\frac{S}{\frac{2\times 2S+S}{6V}}$$

Do the multiplications in 2\times 2S+S.

$$\frac{S}{\frac{4S+S}{6V}}$$

Combine like terms in 4S+S.

$$\frac{S}{\frac{5S}{6V}}$$

Divide S by \frac{5S}{6V} by multiplying S by the reciprocal of \frac{5S}{6V}.

$$\frac{S\times 6V}{5S}$$

Cancel out S in both numerator and denominator.

$$\frac{6V}{5}$$

Differentiate w.r.t. V

$$\frac{6}{5} = 1\frac{1}{5} = 1.2$$