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

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

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expand 1/(t^2)(1+e^{2t}-2e^t)

expand

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

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

Solution steps

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

\frac{s}{( s + 4 ) ( s + 8 )}

\frac{- x ^{2} + 64}{( x ^{2} + 64 ) ^{2}}

x (18 x^{2} + 23 x y + 18 y^{2} = 19)

\frac{x}{2 π} - \frac{1}{8} (100 - x)

\frac{662}{7} 7 - 23

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