SOLUTION: The original problem is: 5 + 1/x-1/x^2=0 I don't know how they reset it as: 5x^2+x-1=0 Please assist in this determination. Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The original problem is: 5 + 1/x-1/x^2=0 I don't know how they reset it as: 5x^2+x-1=0 Please assist in this determination. Thank you.      Log On


   

Question 190570: The original problem is: 5 + 1/x-1/x^2=0
I don't know how they reset it as: 5x^2+x-1=0
Please assist in this determination. Thank you.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Well, if you started with:
5+%2B+1%2Fx+-+1%2Fx%5E2+=+0
.
To rid yourself of all denominators, multiply BOTH sides by x^2 (common denominator):
x%5E2%285+%2B+1%2Fx+-+1%2Fx%5E2%29+=+x%5E2%280%29
Distributing the x^2:
5%28x%5E2%29+%2B+%281%2Fx%29%28x%5E2%29+-+%281%2Fx%5E2%29%28x%5E2%29+=+0
5x%5E2+%2B+x%5E2%2Fx+-+x%5E2%2Fx%5E2+=+0
Through cancellation we get:
5x%5E2+%2B+x+-+1+=+0