Solve 3/a-2-6/a^2+4

$$\frac { 3 } { a - 2 } - \frac { 6 } { a ^ { 2 } + 4 }$$

Evaluate

$$\frac{3\left(a^{2}-2a+8\right)}{\left(a-2\right)\left(a^{2}+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-2 and a^{2}+4 is \left(a-2\right)\left(a^{2}+4\right). Multiply \frac{3}{a-2} times \frac{a^{2}+4}{a^{2}+4}. Multiply \frac{6}{a^{2}+4} times \frac{a-2}{a-2}.

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

Since \frac{3\left(a^{2}+4\right)}{\left(a-2\right)\left(a^{2}+4\right)} and \frac{6\left(a-2\right)}{\left(a-2\right)\left(a^{2}+4\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\left(a^{2}+4\right)-6\left(a-2\right).

$$\frac{3a^{2}+12-6a+12}{\left(a-2\right)\left(a^{2}+4\right)}$$

Combine like terms in 3a^{2}+12-6a+12.

$$\frac{3a^{2}+24-6a}{\left(a-2\right)\left(a^{2}+4\right)}$$

Expand \left(a-2\right)\left(a^{2}+4\right).

$$\frac{3a^{2}+24-6a}{a^{3}-2a^{2}+4a-8}$$

Factor

$$\frac{3\left(a^{2}-2a+8\right)}{\left(a-2\right)\left(a^{2}+4\right)}$$