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

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

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expand e^{x-1}(1+e^{1-x})

expand

e^{x - 1} (1 + e^{1 - x})

e^{x - 1} + 1

Solution steps

e^{x - 1} (1 + e^{1 - x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x - 1}, b = 1, c = e^{1 - x}

= e^{x - 1} \cdot 1 + e^{x - 1} e^{1 - x}

= 1 \cdot e^{x - 1} + e^{x - 1} e^{1 - x}

Simplify

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

= e^{x - 1} + 1

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