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

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

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

expand

- e^{x} (- e^{- x} x - e^{- x})

x + 1

Solution steps

- e^{x} (- e^{- x} x - e^{- x})

Apply the distributive law:

a (b - c) = ab - a c

a = - e^{x}, b = - e^{- x} x, c = e^{- x}

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

Apply minus-plus rules

- (- a) = a

= e^{x} e^{- x} x + e^{x} e^{- x}

Simplify

e^{x} e^{- x} x + e^{x} e^{- x} : x + 1

= x + 1

\frac{n ( n + 1 )}{4}

\frac{x - 9 ( 3 + x )}{9 - x}

L (3 t + 1) U (t - 1)

\frac{( e ^{x} - x ) ^{3}}{3}

3 ((3, - 2) - 2 (- 1, 1))

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