(6/(x^2-2x-8))+(6/(x+2))=(1/(x-4))

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Solution for (6/(x^2-2x-8))+(6/(x+2))=(1/(x-4)) equation: 


D( x )

x+2 = 0

x^2-(2*x)-8 = 0

x-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x^2-(2*x)-8 = 0

x^2-(2*x)-8 = 0

x^2-2*x-8 = 0

x^2-2*x-8 = 0

DELTA = (-2)^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)+2)/(1*2) or x = (2-36^(1/2))/(1*2)

x = 4 or x = -2

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:-2) U (-2:4) U (4:+oo)

6/(x^2-(2*x)-8)+6/(x+2) = 1/(x-4) // - 1/(x-4)

6/(x^2-(2*x)-8)+6/(x+2)-(1/(x-4)) = 0

6/(x^2-2*x-8)+6/(x+2)-(x-4)^-1 = 0

6/(x^2-2*x-8)+6/(x+2)-1/(x-4) = 0

x^2-2*x-8 = 0

x^2-2*x-8 = 0

x^2-2*x-8 = 0

DELTA = (-2)^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)+2)/(1*2) or x = (2-36^(1/2))/(1*2)

x = 4 or x = -2

(x+2)*(x-4) = 0

6/((x+2)*(x-4))+6/(x+2)-1/(x-4) = 0

6/((x+2)*(x-4))+(6*(x-4))/((x+2)*(x-4))+(-1*(x+2))/((x+2)*(x-4)) = 0

6*(x-4)-1*(x+2)+6 = 0

6*x-x-18-2 = 0

5*x-20 = 0

(5*x-20)/((x+2)*(x-4)) = 0

(5*x-20)/((x+2)*(x-4)) = 0 // * (x+2)*(x-4)

5*x-20 = 0

5*x-20 = 0 // + 20

5*x = 20 // : 5

x = 20/5

x = 4

x in { 4} 

x belongs to the empty set

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