SOLUTION: 1/(x-1)+2 /(x+1)=2

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Question 975277: 1/(x-1)+2 /(x+1)=2
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
1/(x-1)+2 /(x+1)=2
Simplifying we get,
[x+1+2(x-1)]/(x^2-1)=2
3x-1=2x^2-2
2x^2-3x-1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-1=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+17+%29%29%2F2%5C2+=+1.78077640640442
x%5B2%5D+=+%28-%28-3%29-sqrt%28+17+%29%29%2F2%5C2+=+-0.280776406404415

Quadratic expression 2x%5E2%2B-3x%2B-1 can be factored:
2x%5E2%2B-3x%2B-1+=+2%28x-1.78077640640442%29%2A%28x--0.280776406404415%29
Again, the answer is: 1.78077640640442, -0.280776406404415. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-1+%29

x=1.78 or x=-0.28