(x+1)/(3(x-2))=((5x)/(6))+((1)/(x-2))

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Solution for (x+1)/(3(x-2))=((5x)/(6))+((1)/(x-2)) equation: 


D( x )

x-2 = 0

3*(x-2) = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

3*(x-2) = 0

3*(x-2) = 0

x-2 = 0 // + 2

x = 2

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

(x+1)/(3*(x-2)) = 1/(x-2)+(5*x)/6 // - 1/(x-2)+(5*x)/6

(x+1)/(3*(x-2))-(1/(x-2))-((5*x)/6) = 0

(x+1)/(3*(x-2))-(x-2)^-1+(-5/6)*x = 0

(x+1)/(3*(x-2))-1/(x-2)+(-5*x)/6 = 0

(6*(x+1))/(3*6*(x-2))+(-1*3*6)/(3*6*(x-2))+(-5*3*x*(x-2))/(3*6*(x-2)) = 0

6*(x+1)-5*3*x*(x-2)-1*3*6 = 0

6*x-15*x^2+30*x-12 = 0

36*x-15*x^2-12 = 0

36*x-15*x^2-12 = 0

3*(12*x-5*x^2-4) = 0

12*x-5*x^2-4 = 0

DELTA = 12^2-(-5*(-4)*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)-12)/(-5*2) or x = (-64^(1/2)-12)/(-5*2)

x = 2/5 or x = 2

3*(x-2/5)*(x-2) = 0

(3*(x-2/5)*(x-2))/(3*6*(x-2)) = 0

(3*(x-2/5)*(x-2))/(3*6*(x-2)) = 0 // * 3*6*(x-2)

3*(x-2/5)*(x-2) = 0

( x-2/5 )

x-2/5 = 0 // + 2/5

x = 2/5

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = 2/5

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