Solve 1/2x-3/4x+5/6x=

$$\frac { 1 } { 2 x } - \frac { 3 } { 4 x } + \frac { 5 } { 6 x } =$$

Evaluate

$$\frac{7}{12x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 4x is 4x. Multiply \frac{1}{2x} times \frac{2}{2}.

$$\frac{2}{4x}-\frac{3}{4x}+\frac{5}{6x}$$

Since \frac{2}{4x} and \frac{3}{4x} have the same denominator, subtract them by subtracting their numerators. Subtract 3 from 2 to get -1.

$$\frac{-1}{4x}+\frac{5}{6x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4x and 6x is 12x. Multiply \frac{-1}{4x} times \frac{3}{3}. Multiply \frac{5}{6x} times \frac{2}{2}.

$$\frac{-3}{12x}+\frac{5\times 2}{12x}$$

Since \frac{-3}{12x} and \frac{5\times 2}{12x} have the same denominator, add them by adding their numerators.

$$\frac{-3+5\times 2}{12x}$$

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

$$\frac{-3+10}{12x}$$

Do the calculations in -3+10.

$$\frac{7}{12x}$$

Differentiate w.r.t. x

$$-\frac{7}{12x^{2}}$$