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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = - \frac{1}{2}, b = e^{- t}, c = 1

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

Apply minus-plus rules

- (- a) = a

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

Multiply:

1 \cdot \frac{1}{2} = \frac{1}{2}

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

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

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\frac{( 1 - x ^{2} ) ^{2}}{2}

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

\frac{ln ( s )}{s ( s + 1 )}

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