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

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

Evaluate

$$\frac{11}{6x}$$

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}.

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

Since \frac{3\times 2}{2x} and \frac{1}{2x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 2+1.

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

Do the calculations in 6+1.

$$\frac{7}{2x}-\frac{5}{3x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 3x is 6x. Multiply \frac{7}{2x} times \frac{3}{3}. Multiply \frac{5}{3x} times \frac{2}{2}.

$$\frac{7\times 3}{6x}-\frac{5\times 2}{6x}$$

Since \frac{7\times 3}{6x} and \frac{5\times 2}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\times 3-5\times 2}{6x}$$

Do the multiplications in 7\times 3-5\times 2.

$$\frac{21-10}{6x}$$

Do the calculations in 21-10.

$$\frac{11}{6x}$$

Differentiate w.r.t. x

$$-\frac{11}{6x^{2}}$$