(2/(x+4))+(4/(x-2))=((24)/((x+4)*(x-2)))

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Solution for (2/(x+4))+(4/(x-2))=((24)/((x+4)*(x-2))) equation: 


D( x )

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

x+4 = 0

x-2 = 0

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

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

( x+4 )

x+4 = 0 // - 4

x = -4

( x-2 )

x-2 = 0 // + 2

x = 2

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

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

2/(x+4)+4/(x-2) = 24/((x+4)*(x-2)) // - 24/((x+4)*(x-2))

2/(x+4)+4/(x-2)-(24/((x+4)*(x-2))) = 0

2/(x+4)+4/(x-2)-24*(x-2)^-1*(x+4)^-1 = 0

2/(x+4)+4/(x-2)-24/((x-2)*(x+4)) = 0

(2*(x-2))/((x+4)*(x-2))+(4*(x+4))/((x+4)*(x-2))-24/((x+4)*(x-2)) = 0

2*(x-2)+4*(x+4)-24 = 0

6*x-24+12 = 0

6*x-12 = 0

(6*x-12)/((x+4)*(x-2)) = 0

(6*x-12)/((x+4)*(x-2)) = 0 // * (x+4)*(x-2)

6*x-12 = 0

6*x-12 = 0 // + 12

6*x = 12 // : 6

x = 12/6

x = 2

x in { 2} 

x belongs to the empty set

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