Solve 3/x+5/2x+1/3x

$$\frac { 3 } { x } + \frac { 5 } { 2 x } + \frac { 1 } { 3 x }$$

Evaluate

$$\frac{35}{6x}$$

Short Solution Steps

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

$$\frac{3\times 2}{2x}+\frac{5}{2x}+\frac{1}{3x}$$

Since \frac{3\times 2}{2x} and \frac{5}{2x} have the same denominator, add them by adding their numerators.

$$\frac{3\times 2+5}{2x}+\frac{1}{3x}$$

Do the multiplications in 3\times 2+5.

$$\frac{6+5}{2x}+\frac{1}{3x}$$

Do the calculations in 6+5.

$$\frac{11}{2x}+\frac{1}{3x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 3x is 6x. Multiply \frac{11}{2x} times \frac{3}{3}. Multiply \frac{1}{3x} times \frac{2}{2}.

$$\frac{11\times 3}{6x}+\frac{2}{6x}$$

Since \frac{11\times 3}{6x} and \frac{2}{6x} have the same denominator, add them by adding their numerators.

$$\frac{11\times 3+2}{6x}$$

Do the multiplications in 11\times 3+2.

$$\frac{33+2}{6x}$$

Do the calculations in 33+2.

$$\frac{35}{6x}$$

Differentiate w.r.t. x

$$-\frac{35}{6x^{2}}$$