Solve 1/a+1/2a+1/4a

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

Evaluate

$$\frac{7}{4a}$$

Short Solution Steps

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

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

Since \frac{2}{2a} and \frac{1}{2a} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

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

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

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

Since \frac{3\times 2}{4a} and \frac{1}{4a} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 2+1.

$$\frac{6+1}{4a}$$

Do the calculations in 6+1.

$$\frac{7}{4a}$$

Differentiate w.r.t. a

$$-\frac{7}{4a^{2}}$$