(w-5)/(w-1)=(w-7)/(w-3)+1

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Solution for (w-5)/(w-1)=(w-7)/(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-7)/(w-3)+1 // - (w-7)/(w-3)+1

(w-5)/(w-1)-((w-7)/(w-3))-1 = 0

(w-5)/(w-1)+(-1*(w-7))/(w-3)-1 = 0

((w-5)*(w-3))/((w-1)*(w-3))+(-1*(w-7)*(w-1))/((w-1)*(w-3))+(-1*(w-1)*(w-3))/((w-1)*(w-3)) = 0

(w-5)*(w-3)-1*(w-7)*(w-1)-1*(w-1)*(w-3) = 0

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

4*w-w^2+5 = 0

4*w-w^2+5 = 0

4*w-w^2+5 = 0

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

DELTA = 36

DELTA > 0

w = (36^(1/2)-4)/(-1*2) or w = (-36^(1/2)-4)/(-1*2)

w = -1 or w = 5

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

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

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

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

( w+1 )

w+1 = 0 // - 1

w = -1

( w-5 )

w-5 = 0 // + 5

w = 5

w in { -1, 5 }

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