(w-3)/(w-6)=(w+5)/(w-3)+1

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


D( w )

w-3 = 0

w-6 = 0

w-3 = 0

w-3 = 0

w-3 = 0 // + 3

w = 3

w-6 = 0

w-6 = 0

w-6 = 0 // + 6

w = 6

w in (-oo:3) U (3:6) U (6:+oo)

(w-3)/(w-6) = (w+5)/(w-3)+1 // - (w+5)/(w-3)+1

(w-3)/(w-6)-((w+5)/(w-3))-1 = 0

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

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

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

9*w-w^2-5*w-18+39 = 0

4*w-w^2+21 = 0

4*w-w^2+21 = 0

4*w-w^2+21 = 0

DELTA = 4^2-(-1*4*21)

DELTA = 100

DELTA > 0

w = (100^(1/2)-4)/(-1*2) or w = (-100^(1/2)-4)/(-1*2)

w = -3 or w = 7

(w+3)*(w-7) = 0

((w+3)*(w-7))/((w-6)*(w-3)) = 0

((w+3)*(w-7))/((w-6)*(w-3)) = 0 // * (w-6)*(w-3)

(w+3)*(w-7) = 0

( w+3 )

w+3 = 0 // - 3

w = -3

( w-7 )

w-7 = 0 // + 7

w = 7

w in { -3, 7 }

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