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

The solution to expand (e^t(2-t))/((1-t)^2) is (2e^t-e^tt)/(1-2t+t^2)

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expand (e^t(2-t))/((1-t)^2)

expand

\frac{e ^{t} ( 2 - t )}{( 1 - t ) ^{2}}

\frac{2 e ^{t} - e ^{t} t}{1 - 2 t + t ^{2}}

Solution steps

\frac{e ^{t} ( 2 - t )}{( 1 - t ) ^{2}}

(1 - t)^{2} = 1 - 2 t + t^{2}

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

Expand

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

= \frac{2 e ^{t} - e ^{t} t}{1 - 2 t + t ^{2}}

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What is expand (e^t(2-t))/((1-t)^2) ?
The solution to expand (e^t(2-t))/((1-t)^2) is (2e^t-e^tt)/(1-2t+t^2)