Solve t+2/t+1/t^3

$$t+ \frac{ 2 }{ t } + \frac{ 1 }{ { t }^{ 3 } }$$

Evaluate

$$\frac{\left(t^{2}+1\right)^{2}}{t^{3}}$$

Short Solution Steps

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

$$\frac{tt}{t}+\frac{2}{t}+\frac{1}{t^{3}}$$

Since \frac{tt}{t} and \frac{2}{t} have the same denominator, add them by adding their numerators.

$$\frac{tt+2}{t}+\frac{1}{t^{3}}$$

Do the multiplications in tt+2.

$$\frac{t^{2}+2}{t}+\frac{1}{t^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t and t^{3} is t^{3}. Multiply \frac{t^{2}+2}{t} times \frac{t^{2}}{t^{2}}.

$$\frac{\left(t^{2}+2\right)t^{2}}{t^{3}}+\frac{1}{t^{3}}$$

Since \frac{\left(t^{2}+2\right)t^{2}}{t^{3}} and \frac{1}{t^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(t^{2}+2\right)t^{2}+1}{t^{3}}$$

Do the multiplications in \left(t^{2}+2\right)t^{2}+1.

$$\frac{t^{4}+2t^{2}+1}{t^{3}}$$

Factor

$$\frac{\left(t^{2}+1\right)^{2}}{t^{3}}$$