(x-1)/(x-6)-(1/2)=(11-x)/(x-6)

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Solution for (x-1)/(x-6)-(1/2)=(11-x)/(x-6) equation: 


D( x )

x-6 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

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

(x-1)/(x-6)-(1/2) = (11-x)/(x-6) // - (11-x)/(x-6)

(x-1)/(x-6)-((11-x)/(x-6))-(1/2) = 0

(x-1)/(x-6)-((11-x)/(x-6))-1/2 = 0

(x-1)/(x-6)+(-1*(11-x))/(x-6)-1/2 = 0

(2*(x-1))/(2*(x-6))+(-1*2*(11-x))/(2*(x-6))+(-1*(x-6))/(2*(x-6)) = 0

2*(x-1)-1*2*(11-x)-1*(x-6) = 0

4*x-x-24+6 = 0

3*x-18 = 0

(3*x-18)/(2*(x-6)) = 0

(3*x-18)/(2*(x-6)) = 0 // * 2*(x-6)

3*x-18 = 0

3*x-18 = 0 // + 18

3*x = 18 // : 3

x = 18/3

x = 6

x in { 6} 

x belongs to the empty set

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