SOLUTION: solve: 3+1/x-2=2x-3/x-2

Question 35587: solve:
3+1/x-2=2x-3/x-2
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
3+(1/x-2)=2x-(3/x-2) original
(x-2)(3+(1/x-2))=(x-2)(2x-(3/x-2))
3x-6+1=2x^2-4x-3
0=2x^2-7x+2

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=33 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.18614066163451, 0.313859338365493. Here's your graph:

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