1/(x-2)-1(x-1)=1/6

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Solution for 1/(x-2)-1(x-1)=1/6 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)

1/(x-2)-(1*(x-1)) = 1/6 // - 1/6

1/(x-2)-(1*(x-1))-(1/6) = 0

1/(x-2)-x-1/6+1 = 0

(1*6)/(6*(x-2))+(6*(-x)*(x-2))/(6*(x-2))+(-1*(x-2))/(6*(x-2))+(1*6*(x-2))/(6*(x-2)) = 0

6*(-x)*(x-2)-1*(x-2)+1*6*(x-2)+1*6 = 0

12*x-6*x^2-x+6*x-12+2+6 = 0

11*x-6*x^2+6*x-12+8 = 0

17*x-6*x^2-4 = 0

17*x-6*x^2-4 = 0

17*x-6*x^2-4 = 0

DELTA = 17^2-(-6*(-4)*4)

DELTA = 193

DELTA > 0

x = (193^(1/2)-17)/(-6*2) or x = (-193^(1/2)-17)/(-6*2)

x = (193^(1/2)-17)/(-12) or x = (193^(1/2)+17)/12

(x-((193^(1/2)-17)/(-12)))*(x-((193^(1/2)+17)/12)) = 0

((x-((193^(1/2)-17)/(-12)))*(x-((193^(1/2)+17)/12)))/(6*(x-2)) = 0

((x-((193^(1/2)-17)/(-12)))*(x-((193^(1/2)+17)/12)))/(6*(x-2)) = 0 // * 6*(x-2)

(x-((193^(1/2)-17)/(-12)))*(x-((193^(1/2)+17)/12)) = 0

( x-((193^(1/2)+17)/12) )

x-((193^(1/2)+17)/12) = 0 // + (193^(1/2)+17)/12

x = (193^(1/2)+17)/12

( x-((193^(1/2)-17)/(-12)) )

x-((193^(1/2)-17)/(-12)) = 0 // + (193^(1/2)-17)/(-12)

x = (193^(1/2)-17)/(-12)

x in { (193^(1/2)+17)/12, (193^(1/2)-17)/(-12) }

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