Solve 1/6a+b/3a^2-5/2ab

$$\frac { 1 } { 6 a } + \frac { b } { 3 a ^ { 2 } } - \frac { 5 } { 2 a b }$$

Evaluate

$$\frac{b}{3a^{2}}+\frac{1}{6a}-\frac{5}{2ab}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6a and 3a^{2} is 6a^{2}. Multiply \frac{1}{6a} times \frac{a}{a}. Multiply \frac{b}{3a^{2}} times \frac{2}{2}.

$$\frac{a}{6a^{2}}+\frac{2b}{6a^{2}}-\frac{5}{2ab}$$

Since \frac{a}{6a^{2}} and \frac{2b}{6a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{a+2b}{6a^{2}}-\frac{5}{2ab}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6a^{2} and 2ab is 6ba^{2}. Multiply \frac{a+2b}{6a^{2}} times \frac{b}{b}. Multiply \frac{5}{2ab} times \frac{3a}{3a}.

$$\frac{\left(a+2b\right)b}{6ba^{2}}-\frac{5\times 3a}{6ba^{2}}$$

Since \frac{\left(a+2b\right)b}{6ba^{2}} and \frac{5\times 3a}{6ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(a+2b\right)b-5\times 3a}{6ba^{2}}$$

Do the multiplications in \left(a+2b\right)b-5\times 3a.

$$\frac{ab+2b^{2}-15a}{6ba^{2}}$$

Factor

$$\frac{ab-15a+2b^{2}}{6ba^{2}}$$