Question 306759
[((x+1)/(x-1)+1)/((x+1)/(x-1)-1)]^5 

Let's look at the expression that is being raised to the 5th power. A common denominator for the terms is x-1. Rewriting 1 as (x-1)/(x-1):

((x+1)/(x-1)) + (x-1)/(x-1) / ((x+1)/(x-1) - (x-1)/(x-1))

Combining terms we have:

(((x+1) + (x+1))/(x-1)) / (((x+1) - (x-1))/(x-1)) =
((2x+2)/(x-1)) / (2/(x-1))

Multiplying numerator and denominator above by (x-1) gives:

(2x+2)/2 = 2*(x+1)/2 = x+1

So the original problem reduces to (x+1)^5

You could expand out (x+1)^5.