(x+6)/(x-5)+1=11/(x-5)

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Solution for (x+6)/(x-5)+1=11/(x-5) equation: 


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

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

(x+6)/(x-5)+1 = 11/(x-5) // - 11/(x-5)

(x+6)/(x-5)-(11/(x-5))+1 = 0

(x+6)/(x-5)-11*(x-5)^-1+1 = 0

(x+6)/(x-5)-11/(x-5)+1 = 0

(x+6)/(x-5)-11/(x-5)+(1*(x-5))/(x-5) = 0

1*(x-5)+x-11+6 = 0

x+x-5-5 = 0

2*x-10 = 0

(2*x-10)/(x-5) = 0

(2*x-10)/(x-5) = 0 // * x-5

2*x-10 = 0

2*x-10 = 0 // + 10

2*x = 10 // : 2

x = 10/2

x = 5

x in { 5} 

x belongs to the empty set

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