x/(x^2-16)=4/(x^2-16)-2/(x+4)

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Solution for x/(x^2-16)=4/(x^2-16)-2/(x+4) equation: 


D( x )

x+4 = 0

x^2-16 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x^2-16 = 0

x^2-16 = 0

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

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

x/(x^2-16) = 4/(x^2-16)-(2/(x+4)) // - 4/(x^2-16)-(2/(x+4))

x/(x^2-16)-(4/(x^2-16))+2/(x+4) = 0

x/(x^2-16)-4*(x^2-16)^-1+2/(x+4) = 0

x/(x^2-16)-4/(x^2-16)+2/(x+4) = 0

(x*(x+4))/((x^2-16)*(x+4))+(-4*(x+4))/((x^2-16)*(x+4))+(2*(x^2-16))/((x^2-16)*(x+4)) = 0

x*(x+4)-4*(x+4)+2*(x^2-16) = 0

x^2+2*x^2-32-16 = 0

3*x^2-48 = 0

(3*x^2-48)/((x^2-16)*(x+4)) = 0

(3*x^2-48)/((x^2-16)*(x+4)) = 0 // * (x^2-16)*(x+4)

3*x^2-48 = 0

3*x^2 = 48 // : 3

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x in { 4} 

x in { -4} 

x belongs to the empty set

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