(w/(w-3))-((3w)/(3w-2))=((w-3)/((3w^2)-11w+6))

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Solution for (w/(w-3))-((3w)/(3w-2))=((w-3)/((3w^2)-11w+6)) equation: 


D( w )

w-3 = 0

3*w^2-(11*w)+6 = 0

3*w-2 = 0

w-3 = 0

w-3 = 0

w-3 = 0 // + 3

w = 3

3*w^2-(11*w)+6 = 0

3*w^2-(11*w)+6 = 0

3*w^2-11*w+6 = 0

3*w^2-11*w+6 = 0

DELTA = (-11)^2-(3*4*6)

DELTA = 49

DELTA > 0

w = (49^(1/2)+11)/(2*3) or w = (11-49^(1/2))/(2*3)

w = 3 or w = 2/3

3*w-2 = 0

3*w-2 = 0

3*w-2 = 0 // + 2

3*w = 2 // : 3

w = 2/3

w in (-oo:2/3) U (2/3:3) U (3:+oo)

w/(w-3)-((3*w)/(3*w-2)) = (w-3)/(3*w^2-(11*w)+6) // - (w-3)/(3*w^2-(11*w)+6)

w/(w-3)-((3*w)/(3*w-2))-((w-3)/(3*w^2-(11*w)+6)) = 0

w/(w-3)-3*w*(3*w-2)^-1-((w-3)/(3*w^2-11*w+6)) = 0

w/(w-3)+(-3*w)/(3*w-2)+(-1*(w-3))/(3*w^2-11*w+6) = 0

3*w^2-11*w+6 = 0

3*w^2-11*w+6 = 0

3*w^2-11*w+6 = 0

DELTA = (-11)^2-(3*4*6)

DELTA = 49

DELTA > 0

w = (49^(1/2)+11)/(2*3) or w = (11-49^(1/2))/(2*3)

w = 3 or w = 2/3

(w-2/3)*(w-3) = 0

w/(w-3)+(-3*w)/(3*w-2)+(-1*(w-3))/((w-2/3)*(w-3)) = 0

(w*(3*w-2)*(w-2/3))/((w-3)*(3*w-2)*(w-2/3))+(-3*w*(w-3)*(w-2/3))/((w-3)*(3*w-2)*(w-2/3))+(-1*(w-3)*(3*w-2))/((w-3)*(3*w-2)*(w-2/3)) = 0

w*(3*w-2)*(w-2/3)-3*w*(w-3)*(w-2/3)-1*(w-3)*(3*w-2) = 0

7*w^2-3*w^2-14/3*w+11*w-6 = 0

4*w^2+19/3*w-6 = 0

4*w^2+19/3*w-6 = 0

4*w^2+19/3*w-6 = 0

DELTA = (19/3)^2-(-6*4*4)

DELTA = 1225/9

DELTA > 0

w = ((1225/9)^(1/2)-19/3)/(2*4) or w = (-(1225/9)^(1/2)-19/3)/(2*4)

w = 2/3 or w = -9/4

(w+9/4)*(w-2/3) = 0

((w+9/4)*(w-2/3))/((w-3)*(3*w-2)*(w-2/3)) = 0

((w+9/4)*(w-2/3))/((w-3)*(3*w-2)*(w-2/3)) = 0 // * (w-3)*(3*w-2)*(w-2/3)

(w+9/4)*(w-2/3) = 0

( w+9/4 )

w+9/4 = 0 // - 9/4

w = -9/4

( w-2/3 )

w-2/3 = 0 // + 2/3

w = 2/3

w in { 2/3} 

w = -9/4

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