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

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:

The LCD in the denominator is also , so:

Collect like terms:

Factor from the numerator of the numerator:

Use

to write:

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:

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