(x^2+x-6)/(x-2)=x

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Solution for (x^2+x-6)/(x-2)=x equation: 


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

(x^2+x-6)/(x-2) = x // - x

(x^2+x-6)/(x-2)-x = 0

(x^2+x-6)/(x-2)+(-x*(x-2))/(x-2) = 0

x^2-x*(x-2)+x-6 = 0

3*x-6 = 0

(3*x-6)/(x-2) = 0

(3*x-6)/(x-2) = 0 // * x-2

3*x-6 = 0

3*x-6 = 0 // + 6

3*x = 6 // : 3

x = 6/3

x = 2

x in { 2} 

x belongs to the empty set

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