Solve a^2/a-3+9/3a

$$\frac { a ^ { 2 } } { a - 3 } + \frac { 9 } { 3 a }$$

Evaluate

$$\frac{a^{3}+3a-9}{a\left(a-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-3 and 3a is 3a\left(a-3\right). Multiply \frac{a^{2}}{a-3} times \frac{3a}{3a}. Multiply \frac{9}{3a} times \frac{a-3}{a-3}.

$$\frac{a^{2}\times 3a}{3a\left(a-3\right)}+\frac{9\left(a-3\right)}{3a\left(a-3\right)}$$

Since \frac{a^{2}\times 3a}{3a\left(a-3\right)} and \frac{9\left(a-3\right)}{3a\left(a-3\right)} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}\times 3a+9\left(a-3\right)}{3a\left(a-3\right)}$$

Do the multiplications in a^{2}\times 3a+9\left(a-3\right).

$$\frac{3a^{3}+9a-27}{3a\left(a-3\right)}$$

Factor the expressions that are not already factored in \frac{3a^{3}+9a-27}{3a\left(a-3\right)}.

$$\frac{3\left(a^{3}+3a-9\right)}{3a\left(a-3\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{a^{3}+3a-9}{a\left(a-3\right)}$$

Expand a\left(a-3\right).

$$\frac{a^{3}+3a-9}{a^{2}-3a}$$

Differentiate w.r.t. a

$$\frac{a^{4}-6a^{3}-3a^{2}+18a-27}{\left(a\left(a-3\right)\right)^{2}}$$