SOLUTION: Solve the following and indicate the solution set: (1/x^2) * (x^2-x/x^2-1) + (2x-2/x+1) ___________ ___________ ______ = 0 (1/x^2+x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the following and indicate the solution set: (1/x^2) * (x^2-x/x^2-1) + (2x-2/x+1) ___________ ___________ ______ = 0 (1/x^2+x)      Log On


   

Question 737739: Solve the following and indicate the solution set:
(1/x^2) * (x^2-x/x^2-1) + (2x-2/x+1)
______________________________ = 0
(1/x^2+x)
Answer by Susan-math(40) About Me  (Show Source):
You can put this solution on YOUR website!
Clean up the numerator:

and
%282x-2%29%2F%28x%2B1%29=%282%28x-1%29%29%2F%28x%2B1%29
Combine:
1%2F%28x%28x%2B1%29%29%2B%282%28x-1%29%29%2F%28x%2B1%29with Least common denominator x%28x%2B1%29

Clean up the denominator:
1%2F%28x%5E2%2Bx%29=1%2F%28x%28x%2B1%29%29
Now we have:
%28%28%282x%5E2-2x%2B1%29%2F%28x%28x%2B1%29%29%29%2F%281%2F%28x%28x%2B1%29%29%29%29which is
%28%282x%5E2-2x%2B1%29%2F%28x%28x%2B1%29%29%29%2A%28%28x%28x%2B1%29%29%2F1%29
After cancelling:
2x%5E2-2x%2B1=0which has two roots: %281%2Bi%29%2F2,%281-i%29%2F2