What is expand (t^2(t+1))/((t-2)^3) ?

The solution to expand (t^2(t+1))/((t-2)^3) is (t^3+t^2)/(t^3-6t^2+12t-8)

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expand (t^2(t+1))/((t-2)^3)

expand

\frac{t ^{2} ( t + 1 )}{( t - 2 ) ^{3}}

\frac{t ^{3} + t ^{2}}{t ^{3} - 6 t ^{2} + 12 t - 8}

Solution steps

\frac{t ^{2} ( t + 1 )}{( t - 2 ) ^{3}}

(t - 2)^{3} = t^{3} - 6 t^{2} + 12 t - 8

= \frac{t ^{2} ( t + 1 )}{t ^{3} - 6 t ^{2} + 12 t - 8}

Expand

t^{2} (t + 1) : t^{3} + t^{2}

= \frac{t ^{3} + t ^{2}}{t ^{3} - 6 t ^{2} + 12 t - 8}

\frac{8 ( - x + 51 )}{17}

\frac{x ^{2} + 2 x - 2}{( x + 1 ) ( x - 2 )}

(e^{2 t} + e^{- 2 t} + 2)^{2}

(- 5 x - 3) (2 x + 1)^{''}

7 + \frac{1}{5}

What is expand (t^2(t+1))/((t-2)^3) ?
The solution to expand (t^2(t+1))/((t-2)^3) is (t^3+t^2)/(t^3-6t^2+12t-8)