SOLUTION: I am trying to figure out how to start this problem. I saw it and I immediately was confused. Please help me solve this equation: {{{ [((x+1)/(x-1)+1)/((x+1)/(x-1)-1)]^5 }}}

Question 306759: I am trying to figure out how to start this problem. I saw it and I immediately was confused. Please help me solve this equation: AMP Parsing Error of [ [((x+1)/(x-1)+1)/((x+1)/(x-1)-1)]^5 ]: Invalid expression '[((x+1)/(x-1)+1)/((x+1)/(x-1)-1)]^5': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 203. .

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
[((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.

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