SOLUTION: I'm having a hard time understanding this kind of problem....I'll try to type it out as best as I can. Any help would be appreciated. Thank you..
Complex Rational Expressions.
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Question 239400: I'm having a hard time understanding this kind of problem....I'll try to type it out as best as I can. Any help would be appreciated. Thank you..
Complex Rational Expressions...
Simplify
[x+1/x-1 + 1]^5
_______________
[x+1/x-1 - 1]
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You really need to use parentheses more because I am having to guess at what you mean.
I think you are trying to represent
^5}{\left(\frac{x+1}{x-1}\ -\ 1\right)})
If this is correct, you should have represented it as:
[((x+1)/(x-1)) + 1]^5
_______________
[((x+1)/(x-1)) - 1]
Continuing on that presumption, begin with the numerator. The LCD in the numerator is 
, so:
}{x-1}\right)^5}{\left(\frac{x+1}{x-1}\ -\ 1\right)})
The LCD in the denominator is also , so:
}{x-1}\right)^5}{\left(\frac{x+1-(x-1)}{x-1}\right)})
Collect like terms:
^5}{\left(\frac{2}{x-1}\right)})
Factor 
from the numerator of the numerator:
^5}{\left(\frac{2}{x-1}\right)}x^5)
Use
to write:
^4\,x^5)
There are a couple of different ways to go from here. If this were an intermediate calculation, I would leave it like it is since this expression is probably easier to manipulate than any expanded version. But you can easily expand it if you like:
^4})
Or go one step further and use the Binomial Theorem to expand the denominator:
Which is 'simplest' becomes a matter of artistic license at this point. Your choice.
John
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