Solve 1/a-5/2a-3/a^2

$$\frac { 1 } { a } - \frac { 5 } { 2 a } - \frac { 3 } { a ^ { 2 } }$$

Evaluate

$$-\frac{3\left(a+2\right)}{2a^{2}}$$

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}.

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

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

$$\frac{-3}{2a}-\frac{3}{a^{2}}$$

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

$$\frac{-3a}{2a^{2}}-\frac{3\times 2}{2a^{2}}$$

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

$$\frac{-3a-3\times 2}{2a^{2}}$$

Do the multiplications in -3a-3\times 2.

$$\frac{-3a-6}{2a^{2}}$$

Factor

$$-\frac{3\left(a+2\right)}{2a^{2}}$$