What is expand-(e^{-t}-e^{-t}t)(e^t) ?

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

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expand-(e^{-t}-e^{-t}t)(e^t)

expand

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

- 1 + t

Solution steps

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

= - (e^{t}) (e^{- t} - e^{- t} t)

Apply the distributive law:

a (b - c) = ab - a c

a = - (e^{t}), b = e^{- t}, c = e^{- t} t

= - (e^{t}) e^{- t} - (- (e^{t})) e^{- t} t

Apply minus-plus rules

- (- a) = a

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

Simplify

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

= - 1 + t

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\frac{x}{( x ^{2} + 9 ) ^{2}}

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