Solve 1/2a-5/4a+6/5a

$$\frac { 1 } { 2 a } - \frac { 5 } { 4 a } + \frac { 6 } { 5 a }$$

Evaluate

$$\frac{9}{20a}$$

Short Solution Steps

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

$$\frac{2}{4a}-\frac{5}{4a}+\frac{6}{5a}$$

Since \frac{2}{4a} and \frac{5}{4a} have the same denominator, subtract them by subtracting their numerators. Subtract 5 from 2 to get -3.

$$\frac{-3}{4a}+\frac{6}{5a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4a and 5a is 20a. Multiply \frac{-3}{4a} times \frac{5}{5}. Multiply \frac{6}{5a} times \frac{4}{4}.

$$\frac{-3\times 5}{20a}+\frac{6\times 4}{20a}$$

Since \frac{-3\times 5}{20a} and \frac{6\times 4}{20a} have the same denominator, add them by adding their numerators.

$$\frac{-3\times 5+6\times 4}{20a}$$

Do the multiplications in -3\times 5+6\times 4.

$$\frac{-15+24}{20a}$$

Do the calculations in -15+24.

$$\frac{9}{20a}$$

Differentiate w.r.t. a

$$-\frac{9}{20a^{2}}$$