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

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

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

expand

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

- 1 + e^{y}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

= - 1 + e^{y}

\frac{3 ( a + b )}{z + 2 ( a + b )}

\frac{x ( x - 3 )}{( x - 2 )}

- cos (3 (1 + 3 X^{2}))

\frac{n + 1}{( n + 2 ) n}

a (x + 1 = y)

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