SOLUTION: Can someone please help me with the complex fraction? (1/x-x^2)-(1/x^2+x)/(1/x+1)+(1/x^2-1)

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Question 171793: Can someone please help me with the complex fraction?
(1/x-x^2)-(1/x^2+x)/(1/x+1)+(1/x^2-1)
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F%28x-x%5E2%29-1%2F%28x%5E2%2Bx%29%29%2F%281%2F%28x%2B1%29%2B1%2F%28x%5E2-1%29%29 Start with the given expression.


%281%2F%28-x%28x-1%29%29-1%2F%28x%5E2%2Bx%29%29%2F%281%2F%28x%2B1%29%2B1%2F%28x%5E2-1%29%29 Factor x-x%5E2 to get x%281-x%29=-x%28x-1%29


%28-1%2F%28x%28x-1%29%29-1%2F%28x%5E2%2Bx%29%29%2F%281%2F%28x%2B1%29%2B1%2F%28x%5E2-1%29%29 Reduce


%28-1%2F%28x%28x-1%29%29-1%2F%28x%28x%2B1%29%29%29%2F%281%2F%28x%2B1%29%2B1%2F%28x%5E2-1%29%29 Factor x%5E2%2Bx to get x%28x%2B1%29


%28-1%2F%28x%28x-1%29%29-1%2F%28x%28x%2B1%29%29%29%2F%281%2F%28x%2B1%29%2B1%2F%28%28x-1%29%28x%2B1%29%29%29 Factor x%5E2-1 to get %28x-1%29%28x%2B1%29


Now take note that the LCD of the inner denominators is x%28x-1%29%28x%2B1%29


%28%28-1%2F%28cross%28x%29cross%28%28x-1%29%29%29%29%28cross%28x%29cross%28%28x-1%29%29%28x%2B1%29%29-%281%2F%28cross%28x%29cross%28%28x%2B1%29%29%29%29%28cross%28x%29%28x-1%29cross%28%28x%2B1%29%29%29%29%2F%28%281%2Fcross%28%28x%2B1%29%29%29%28x%28x-1%29cross%28%28x%2B1%29%29%29%2B%281%2F%28cross%28%28x-1%29%28x%2B1%29%29%29%29%28x%2Across%28%28x-1%29%28x%2B1%29%29%29%29 Multiply EVERY term by the inner LCD to clear out the inner fractions.


%28-1%28x%2B1%29-%28x-1%29%29%2F%28x%28x-1%29%2Bx%29 Simplify


%28-x-1-x%2B1%29%2F%28x%5E2-x%2Bx%29 Distribute


%28-2x%29%2F%28x%5E2%29 Combine like terms.


%28-2x%29%2F%28x%2Ax%29 Factor x%5E2 to get x%2Ax


%28-2%2Ahighlight%28x%29%29%2F%28highlight%28x%29%2Ax%29 Highlight the common terms.


%28-2%2Across%28x%29%29%2F%28cross%28x%29%2Ax%29 Cancel out the common terms.


-2%2F%28x%29 Simplify.


==================================================================

Answer:


So %281%2F%28x-x%5E2%29-1%2F%28x%5E2%2Bx%29%29%2F%281%2F%28x%2B1%29%2B1%2F%28x%5E2-1%29%29 simplifies to -2%2F%28x%29

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Simplfy:
%28%281%2F%28x-x%5E2%29%29+-+%281%2F%28x%5E2%2Bx%29%29%29%2F%28%281%2F%28x%2B1%29%29%2B%281%2F%28x%5E2-1%29%29%29 Now we'll factor some of the denominators to see if we can find the LCD thus allowing us to add/subtract the fractions where so indicated.
%28%281%2Fx%281-x%29%29-%281%2Fx%28x%2B1%29%29%29%2F%281%2F%28x%2B1%29%2B%281%2F%28x-1%29%28x%2B1%29%29%29 The LCD for the fractions in the numerator is:x%28x-1%29%28x%2B1%29 and for the denominator: %28x%2B1%29%28x-1%29, so...
%28%28%28x%2B1%29-%28x-1%29%29%2F%28x%28x-1%29%28x%2B1%29%29%29%2F%28%28%28x-1%29%2B1%29%2F%28%28x%2B1%29%28x-1%29%29%29 To divide fractions, you "copy-flip-flip", that is copy the first fraction, flip the sign from divide to multiply, then flip (invert) the second fraction.
%28%28%28x%2B1%29-%281-x%29%29%2F%28x%2Across%28%28x-1%29%29cross%28%28x%2B1%29%29%29%29%2A%28%28cross%28%28x%2B1%29%29cross%28%28x-1%29%29%29%2F%28%28x-1%29%2B1%29%29 Cancel the indicated factors then simplify.
%28%28%28x%2B1%29-%281-x%29%29%2Fx%29%2A%281%2F%28%28x-1%29%2B1%29%29%29 Simplify further.
%282x%2Fx%29%2A%281%2Fx%29+=+highlight%282%2Fx%29