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

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


D( x )

x-5 = 0

x-6 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x in (-oo:5) U (5:6) U (6:+oo)

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

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

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

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

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

x^2+6*x-11*x-24+30 = 0

x^2-5*x+6 = 0

x^2-5*x+6 = 0

x^2-5*x+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

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

x = 3 or x = 2

(x-2)*(x-3) = 0

((x-2)*(x-3))/((x-6)*(x-5)) = 0

((x-2)*(x-3))/((x-6)*(x-5)) = 0 // * (x-6)*(x-5)

(x-2)*(x-3) = 0

( x-2 )

x-2 = 0 // + 2

x = 2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 2, 3 }

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