The simplified expression of 3/x+1 - 1/x-1 - 2x/x^2+1 is [-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
How to simplify the expression?
The expression is given as
3/x+1 - 1/x-1 - 2x/x^2+1
Take the LCM of the first two terms
So, we have
(3x - 3 - x - 1)/(x^2 - 1) - 2x/x^2+1
This gives
2x - 4/(x^2 - 1) - 2x/x^2+1
Take the LCM
[(2x - 4)(x^2 + 1) -2x(2x^2 - 1)]/(x^4 - 1)
Expand
[2x^3 - 4x^2 + 2x - 4 - 4x^3 + 2]/[x^4 - 1]
Evaluate the like terms
[-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
Hence, the simplified expression of 3/x+1 - 1/x-1 - 2x/x^2+1 is [-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
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