Solve 21/3+21/a^2-a-12

$$\frac { 21 } { 3 } + \frac { 21 } { a ^ { 2 } - a - 12 }$$

Evaluate

$$\frac{7\left(a^{2}-a-9\right)}{\left(a-4\right)\left(a+3\right)}$$

Short Solution Steps

Divide 21 by 3 to get 7.

$$7+\frac{21}{a^{2}-a-12}$$

Factor a^{2}-a-12.

$$7+\frac{21}{\left(a-4\right)\left(a+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{\left(a-4\right)\left(a+3\right)}{\left(a-4\right)\left(a+3\right)}.

$$\frac{7\left(a-4\right)\left(a+3\right)}{\left(a-4\right)\left(a+3\right)}+\frac{21}{\left(a-4\right)\left(a+3\right)}$$

Since \frac{7\left(a-4\right)\left(a+3\right)}{\left(a-4\right)\left(a+3\right)} and \frac{21}{\left(a-4\right)\left(a+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{7\left(a-4\right)\left(a+3\right)+21}{\left(a-4\right)\left(a+3\right)}$$

Do the multiplications in 7\left(a-4\right)\left(a+3\right)+21.

$$\frac{7a^{2}+21a-28a-84+21}{\left(a-4\right)\left(a+3\right)}$$

Combine like terms in 7a^{2}+21a-28a-84+21.

$$\frac{7a^{2}-7a-63}{\left(a-4\right)\left(a+3\right)}$$

Expand \left(a-4\right)\left(a+3\right).

$$\frac{7a^{2}-7a-63}{a^{2}-a-12}$$

Factor

$$\frac{7\left(a-\frac{1-\sqrt{37}}{2}\right)\left(a-\frac{\sqrt{37}+1}{2}\right)}{\left(a-4\right)\left(a+3\right)}$$