4-(3/(w-1))=1/(w-2)

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


D( w )

w-1 = 0

w-2 = 0

w-1 = 0

w-1 = 0

w-1 = 0 // + 1

w = 1

w-2 = 0

w-2 = 0

w-2 = 0 // + 2

w = 2

w in (-oo:1) U (1:2) U (2:+oo)

4-(3/(w-1)) = 1/(w-2) // - 1/(w-2)

4-(3/(w-1))-(1/(w-2)) = 0

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

4-3/(w-1)-1/(w-2) = 0

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

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

4*w^2-4*w-12*w+7+8 = 0

4*w^2-16*w+15 = 0

4*w^2-16*w+15 = 0

4*w^2-16*w+15 = 0

DELTA = (-16)^2-(4*4*15)

DELTA = 16

DELTA > 0

w = (16^(1/2)+16)/(2*4) or w = (16-16^(1/2))/(2*4)

w = 5/2 or w = 3/2

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

((w-3/2)*(w-5/2))/((w-1)*(w-2)) = 0

((w-3/2)*(w-5/2))/((w-1)*(w-2)) = 0 // * (w-1)*(w-2)

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

( w-3/2 )

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

w = 3/2

( w-5/2 )

w-5/2 = 0 // + 5/2

w = 5/2

w in { 3/2, 5/2 }

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