Solve 8a/a^2+4a-12-4/a-2=

$$\frac { 8 a } { a ^ { 2 } + 4 a - 12 } - \frac { 4 } { a - 2 } =$$

Evaluate

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

Short Solution Steps

Factor a^{2}+4a-12.

$$\frac{8a}{\left(a-2\right)\left(a+6\right)}-\frac{4}{a-2}$$

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

$$\frac{8a}{\left(a-2\right)\left(a+6\right)}-\frac{4\left(a+6\right)}{\left(a-2\right)\left(a+6\right)}$$

Since \frac{8a}{\left(a-2\right)\left(a+6\right)} and \frac{4\left(a+6\right)}{\left(a-2\right)\left(a+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8a-4\left(a+6\right)}{\left(a-2\right)\left(a+6\right)}$$

Do the multiplications in 8a-4\left(a+6\right).

$$\frac{8a-4a-24}{\left(a-2\right)\left(a+6\right)}$$

Combine like terms in 8a-4a-24.

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

Expand \left(a-2\right)\left(a+6\right).

$$\frac{4a-24}{a^{2}+4a-12}$$

Factor

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