Question 202332: Solve equation:
(x+1/x-1) + (2/x)= (x/x+1)
How do I solve this?
Answer by dyakobovitch(40)   (Show Source):
You can put this solution on YOUR website! For the equation, (x+1/x-1) + (2/x)= (x/x+1), your first step is to eliminate your denominator. This can be done by looking for the least common multiple of x, (x-1), and (x+1), which happens to be x(x-1)(x+1).
As such, you want to multiply all three parts of your equation by x(x-1)(x+1). This multiplication preserves the equality of the equation. Your result is x(x-1)(x+1)(x+1)/(x-1) + 2x(x-1)(x+1)/x= x^2(x-1)(x+1)/(x+1), which simplifies to x(x+1)^2 + 2(x-1)(x+1)= x^2(x-1).
Simplifying the quadratic equation, you get x^3+2x^2+x +2x^2-2=x^3-x^2. Your new quadratic equation becomes 5x^2+x-2=0.
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=41 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 0.540312423743285, -0.740312423743285.
Here's your graph:
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