Solve a^2-16-12/a^2-4a

$$a ^ { 2 } - 16 - \frac { 12 } { a ^ { 2 } - 4 a }$$

Evaluate

$$\frac{a^{4}-4a^{3}-16a^{2}+64a-12}{a\left(a-4\right)}$$

Short Solution Steps

Factor a^{2}-4a.

$$a^{2}-16-\frac{12}{a\left(a-4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2}-16 times \frac{a\left(a-4\right)}{a\left(a-4\right)}.

$$\frac{\left(a^{2}-16\right)a\left(a-4\right)}{a\left(a-4\right)}-\frac{12}{a\left(a-4\right)}$$

Since \frac{\left(a^{2}-16\right)a\left(a-4\right)}{a\left(a-4\right)} and \frac{12}{a\left(a-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(a^{2}-16\right)a\left(a-4\right)-12}{a\left(a-4\right)}$$

Do the multiplications in \left(a^{2}-16\right)a\left(a-4\right)-12.

$$\frac{a^{4}-4a^{3}-16a^{2}+64a-12}{a\left(a-4\right)}$$

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

$$\frac{a^{4}-4a^{3}-16a^{2}+64a-12}{a^{2}-4a}$$

Differentiate w.r.t. a

$$\frac{2\left(a^{5}-8a^{4}+16a^{3}+12a-24\right)}{\left(a\left(a-4\right)\right)^{2}}$$