(u-4)/(u-2)=((u+1)/(u-5))+1

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Solution for (u-4)/(u-2)=((u+1)/(u-5))+1 equation:


D( u )

u-5 = 0

u-2 = 0

u-5 = 0

u-5 = 0

u-5 = 0 // + 5

u = 5

u-2 = 0

u-2 = 0

u-2 = 0 // + 2

u = 2

u in (-oo:2) U (2:5) U (5:+oo)

(u-4)/(u-2) = (u+1)/(u-5)+1 // - (u+1)/(u-5)+1

(u-4)/(u-2)-((u+1)/(u-5))-1 = 0

(u-4)/(u-2)+(-1*(u+1))/(u-5)-1 = 0

((u-4)*(u-5))/((u-2)*(u-5))+(-1*(u+1)*(u-2))/((u-2)*(u-5))+(-1*(u-2)*(u-5))/((u-2)*(u-5)) = 0

(u-4)*(u-5)-1*(u+1)*(u-2)-1*(u-2)*(u-5) = 0

7*u-u^2-8*u-10+22 = 0

12-u^2-u = 0

12-u^2-u = 0

12-u^2-u = 0

DELTA = (-1)^2-(-1*4*12)

DELTA = 49

DELTA > 0

u = (49^(1/2)+1)/(-1*2) or u = (1-49^(1/2))/(-1*2)

u = -4 or u = 3

(u+4)*(u-3) = 0

((u+4)*(u-3))/((u-2)*(u-5)) = 0

((u+4)*(u-3))/((u-2)*(u-5)) = 0 // * (u-2)*(u-5)

(u+4)*(u-3) = 0

( u+4 )

u+4 = 0 // - 4

u = -4

( u-3 )

u-3 = 0 // + 3

u = 3

u in { -4, 3 }

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