(w-5)/(w-1)=(w+2)/(w-3)+1

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


D( w )

w-3 = 0

w-1 = 0

w-3 = 0

w-3 = 0

w-3 = 0 // + 3

w = 3

w-1 = 0

w-1 = 0

w-1 = 0 // + 1

w = 1

w in (-oo:1) U (1:3) U (3:+oo)

(w-5)/(w-1) = (w+2)/(w-3)+1 // - (w+2)/(w-3)+1

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

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

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

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

4*w-w^2-9*w-3+17 = 0

14-w^2-5*w = 0

14-w^2-5*w = 0

14-w^2-5*w = 0

DELTA = (-5)^2-(-1*4*14)

DELTA = 81

DELTA > 0

w = (81^(1/2)+5)/(-1*2) or w = (5-81^(1/2))/(-1*2)

w = -7 or w = 2

(w+7)*(w-2) = 0

((w+7)*(w-2))/((w-1)*(w-3)) = 0

((w+7)*(w-2))/((w-1)*(w-3)) = 0 // * (w-1)*(w-3)

(w+7)*(w-2) = 0

( w+7 )

w+7 = 0 // - 7

w = -7

( w-2 )

w-2 = 0 // + 2

w = 2

w in { -7, 2 }

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