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

The solution to expand (e^t(t^2+1)-2te^t)/((t^2+1)^2) is (e^tt^2+e^t-2e^tt)/(t^4+2t^2+1)

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

expand

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

\frac{e ^{t} t ^{2} + e ^{t} - 2 e ^{t} t}{t ^{4} + 2 t ^{2} + 1}

Solution steps

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

(t^{2} + 1)^{2} = t^{4} + 2 t^{2} + 1

= \frac{e ^{t} ( t ^{2} + 1 ) - 2 e ^{t} t}{t ^{4} + 2 t ^{2} + 1}

Expand

e^{t} (t^{2} + 1) - 2 t e^{t} : e^{t} t^{2} + e^{t} - 2 t e^{t}

= \frac{e ^{t} t ^{2} + e ^{t} - 2 e ^{t} t}{t ^{4} + 2 t ^{2} + 1}

e^{t (- \frac{1}{a} + i)}

\frac{- 6 x + 17}{( x + 3 ) ( 2 x - 1 )}

- \frac{x ^{4} - 10 x ^{3} - 13 x ^{2} + 60 x + 36}{( x ^{2} - 5 x + 6 ) ^{2}}

\frac{s + 1}{s ( s ^{2} - 7 s )}

2 x^{2} y sin (x^{2} + y^{2}) + 2 a x sin (a (x^{2} + y^{2}))

What is expand (e^t(t^2+1)-2te^t)/((t^2+1)^2) ?
The solution to expand (e^t(t^2+1)-2te^t)/((t^2+1)^2) is (e^tt^2+e^t-2e^tt)/(t^4+2t^2+1)