How do you simplify # (e^8 - e^(-8))/(e^4 - e^(-4))#?

1 Answer
Annie
Nov 6, 2016

#(e^8+1)/e^4#

Explanation:

Look at the numerator of the expression
#e^8-e^-8#
=#e^8-1/e^8 # now write as one fraction
=#(e^16-1)/e^8#now factorise the numerator
=#((e^8-1)(e^8+1))/e^8#

Now rearrange the denominator of our original expression

#e^4-e^-4#
=#e^4-1/e^4#
=#(e^8-1)/e^4#

=#((e^8-1)(e^8+1))/e^8#divided by #(e^8-1)/e^4#
=#(e^8+1)/e^4#

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