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

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