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

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Solution for (2x/(x^2-16))=(2/(x+4))-(1/(x-4)) equation: 


D( x )

x+4 = 0

x^2-16 = 0

x-4 = 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-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

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

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

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

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

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

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

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

x^3+8*x^2+4*x^2-16*x-128-64 = 0

x^3+12*x^2-16*x-192 = 0

x^3+12*x^2-16*x-192 = 0

x^3+12*x^2-16*x-192

x^2*(x+12)-16*x-192

x^2*(x+12)-16*(x+12)

(x^2-16)*(x+12)

((x^2-16)*(x+12))/((x^2-16)*(x+4)*(x-4)) = 0

((x^2-16)*(x+12))/((x^2-16)*(x+4)*(x-4)) = 0 // * (x^2-16)*(x+4)*(x-4)

(x^2-16)*(x+12) = 0

( x+12 )

x+12 = 0 // - 12

x = -12

( x^2-16 )

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x in { 4} 

x in { -4} 

x = -12

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