Sinplifying complex fractions: (2x)/(x-1) + (x+1)/(-x) / ...

[MathHatesMe]

Hey. I need as much help as I can get from this problem. I have a lot of trouble in Algebra and I dont really even know where to begin. Do I find a common denominator first?

. . .[ (2x) / (x - 1) + (x + 1) / (-x) ] / [ (4x) / (x + 1) - (2x + 2) / (3x) ]

:?
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Edited by stapel -- Reason for edit: formatting

 

[stapel]

You have one big (and ugly) fraction containing four sub-fractions. One method of simplifying this expression would be to find the common denominator for all four sub-fractions, and multiply, top and bottom, by this expression.

Eliz.

 

[Denis]

Re: Sinplifying complex fractions: (2x)/(x-1) + (x+1)/(-x) /

[ (2x) / (x - 1) + (x + 1) / (-x) ] / [ (4x) / (x + 1) - (2x + 2) / (3x) ]

Rewrite , to get rid of (-x) and simplify 2x + 2:
[ (2x) / (x - 1) - (x + 1) / x ] / [ (4x) / (x + 1) - 2(x + 1) / (3x) ]

Keep it manageable: a = x + 1, b = x - 1:
[ (2x) / b - a / x ] / [ (4x) / a - 2a / (3x) ]

Good luck; as Stapel says, it'll be UGLY.