Solve h(t)=t/(t^3+t^5)(t^5+1)

$$h ( t ) = \frac { t } { ( t ^ { 3 } + t ^ { 5 } ) ( t ^ { 5 } + 1 ) }$$

Evaluate

$$\frac{1}{t^{2}\left(t^{2}+1\right)\left(t^{5}+1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{t}{\left(t+1\right)\left(t^{2}+1\right)t^{3}\left(t^{4}-t^{3}+t^{2}-t+1\right)}$$

Cancel out t in both numerator and denominator.

$$\frac{1}{\left(t+1\right)t^{2}\left(t^{2}+1\right)\left(t^{4}-t^{3}+t^{2}-t+1\right)}$$

Expand the expression.

$$\frac{1}{t^{9}+t^{7}+t^{4}+t^{2}}$$

Expand

$$\frac{1}{t^{2}\left(t^{2}+1\right)\left(t^{5}+1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{t}{\left(t+1\right)\left(t^{2}+1\right)t^{3}\left(t^{4}-t^{3}+t^{2}-t+1\right)}$$

Cancel out t in both numerator and denominator.

$$\frac{1}{\left(t+1\right)t^{2}\left(t^{2}+1\right)\left(t^{4}-t^{3}+t^{2}-t+1\right)}$$

Expand the expression.

$$\frac{1}{t^{9}+t^{7}+t^{4}+t^{2}}$$