SOLUTION: Will you please help me with this rational equation? I got it wrong on my test but still am having trouble solving it. I appreciate you taking the time to help me. x/x^2-1+2/x-

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Question 286145: Will you please help me with this rational equation? I got it wrong on my test but still am having trouble solving it. I appreciate you taking the time to help me.
x/x^2-1+2/x-1=1+1/2x-2
I know the LCD is 2(x+1)(x-1). I multiplied every numerator by the missing factor and came up with totally the wrong answer. I am not sure what to do with the "+1."
Tina
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!

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The idea of the LCD is to get rid of the denominators...so cancel the terms you can:
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Of course we can eliminate any '1' that is a multiplier, and cancel the 2/2. And 2*2 is 4.
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Subtract 6x from both sides.
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Subtract 4 from both sides.
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This cannot be factored easily, so the quadratic equation can be used.
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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=65 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.26556443707464, -0.765564437074637. Here's your graph:
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