Solve 3/4a+1/2a-2/3a

$$\frac { 3 } { 4 a } + \frac { 1 } { 2 a } - \frac { 2 } { 3 a }$$

Evaluate

$$\frac{7}{12a}$$

Short Solution Steps

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

$$\frac{3}{4a}+\frac{2}{4a}-\frac{2}{3a}$$

Since \frac{3}{4a} and \frac{2}{4a} have the same denominator, add them by adding their numerators. Add 3 and 2 to get 5.

$$\frac{5}{4a}-\frac{2}{3a}$$

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

$$\frac{5\times 3}{12a}-\frac{2\times 4}{12a}$$

Since \frac{5\times 3}{12a} and \frac{2\times 4}{12a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 3-2\times 4}{12a}$$

Do the multiplications in 5\times 3-2\times 4.

$$\frac{15-8}{12a}$$

Do the calculations in 15-8.

$$\frac{7}{12a}$$

Differentiate w.r.t. a

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