((6x)/(x^2-4))=((12)/(x^2-4))-((4)/(x+2))

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Solution for ((6x)/(x^2-4))=((12)/(x^2-4))-((4)/(x+2)) equation: 


D( x )

x+2 = 0

x^2-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

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

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

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

(6*x)/(x^2-4)-12*(x^2-4)^-1+4/(x+2) = 0

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

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

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

6*x^2+4*x^2-24-16 = 0

10*x^2-40 = 0

(10*x^2-40)/((x^2-4)*(x+2)) = 0

(10*x^2-40)/((x^2-4)*(x+2)) = 0 // * (x^2-4)*(x+2)

10*x^2-40 = 0

10*x^2 = 40 // : 10

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in { 2} 

x in { -2} 

x belongs to the empty set

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