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Write in simplest form.

Solution

( e^x - 1) / (e^-x - 1)

e^-x can be written as 1/e^x

( e^x - 1) / ( 1/e^x -1 )

= e^x ( e^x - 1) / (1 - e^x )

= - e^x ( 1 - e^x ) / (1 - e^x )

cancelling the common factors from top and bottom we get

= - e^x