((w)/(w-2))-((3w)/(3w-2))=((w-1)/(3w^2-8w+4))

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Solution for ((w)/(w-2))-((3w)/(3w-2))=((w-1)/(3w^2-8w+4)) equation: 


D( w )

3*w^2-(8*w)+4 = 0

3*w-2 = 0

w-2 = 0

3*w^2-(8*w)+4 = 0

3*w^2-(8*w)+4 = 0

3*w^2-8*w+4 = 0

3*w^2-8*w+4 = 0

DELTA = (-8)^2-(3*4*4)

DELTA = 16

DELTA > 0

w = (16^(1/2)+8)/(2*3) or w = (8-16^(1/2))/(2*3)

w = 2 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-2 = 0

w-2 = 0

w-2 = 0 // + 2

w = 2

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

w/(w-2)-((3*w)/(3*w-2)) = (w-1)/(3*w^2-(8*w)+4) // - (w-1)/(3*w^2-(8*w)+4)

w/(w-2)-((3*w)/(3*w-2))-((w-1)/(3*w^2-(8*w)+4)) = 0

w/(w-2)-3*w*(3*w-2)^-1-((w-1)/(3*w^2-8*w+4)) = 0

w/(w-2)+(-3*w)/(3*w-2)+(-1*(w-1))/(3*w^2-8*w+4) = 0

3*w^2-8*w+4 = 0

3*w^2-8*w+4 = 0

3*w^2-8*w+4 = 0

DELTA = (-8)^2-(3*4*4)

DELTA = 16

DELTA > 0

w = (16^(1/2)+8)/(2*3) or w = (8-16^(1/2))/(2*3)

w = 2 or w = 2/3

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

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

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

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

4*w^2-3*w^2-8/3*w+5*w-2 = 0

w^2+7/3*w-2 = 0

w^2+7/3*w-2 = 0

w^2+7/3*w-2 = 0

DELTA = (7/3)^2-(-2*1*4)

DELTA = 121/9

DELTA > 0

w = ((121/9)^(1/2)-7/3)/(1*2) or w = (-(121/9)^(1/2)-7/3)/(1*2)

w = 2/3 or w = -3

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

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

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

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

( w+3 )

w+3 = 0 // - 3

w = -3

( w-2/3 )

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

w = 2/3

w in { 2/3} 

w = -3

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