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

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


D( x )

x-5 = 0

x-3 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:3) U (3:5) U (5:+oo)

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

(x-6)/(x-3)-((x-1)/(x-5))-1 = 0

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

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

(x-6)*(x-5)-1*(x-1)*(x-3)-1*(x-3)*(x-5) = 0

8*x-x^2-7*x-15+27 = 0

x-x^2+12 = 0

x-x^2+12 = 0

x-x^2+12 = 0

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

DELTA = 49

DELTA > 0

x = (49^(1/2)-1)/(-1*2) or x = (-49^(1/2)-1)/(-1*2)

x = -3 or x = 4

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

((x+3)*(x-4))/((x-3)*(x-5)) = 0

((x+3)*(x-4))/((x-3)*(x-5)) = 0 // * (x-3)*(x-5)

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

( x+3 )

x+3 = 0 // - 3

x = -3

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -3, 4 }

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