Solve f(t)=4t^2-12+4/t^2

$$f ( t ) = 4 t ^ { 2 } - 12 + \frac { 4 } { t ^ { 2 } }$$

Evaluate

$$4t^{2}-12+\frac{4}{t^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4t^{2}-12 times \frac{t^{2}}{t^{2}}.

$$\frac{\left(4t^{2}-12\right)t^{2}}{t^{2}}+\frac{4}{t^{2}}$$

Since \frac{\left(4t^{2}-12\right)t^{2}}{t^{2}} and \frac{4}{t^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(4t^{2}-12\right)t^{2}+4}{t^{2}}$$

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

$$\frac{4t^{4}-12t^{2}+4}{t^{2}}$$

Factor

$$\frac{4\left(t^{2}-\frac{3-\sqrt{5}}{2}\right)\left(t^{2}-\frac{\sqrt{5}+3}{2}\right)}{t^{2}}$$