2x/(x^2-16)=3/(x^2-16)-1/(x-4)

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Solution for 2x/(x^2-16)=3/(x^2-16)-1/(x-4) equation: 


D( x )

x^2-16 = 0

x-4 = 0

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) = 3/(x^2-16)-(1/(x-4)) // - 3/(x^2-16)-(1/(x-4))

(2*x)/(x^2-16)-(3/(x^2-16))+1/(x-4) = 0

(2*x)/(x^2-16)-3*(x^2-16)^-1+1/(x-4) = 0

(2*x)/(x^2-16)-3/(x^2-16)+1/(x-4) = 0

(2*x*(x-4))/((x^2-16)*(x-4))+(-3*(x-4))/((x^2-16)*(x-4))+(1*(x^2-16))/((x^2-16)*(x-4)) = 0

2*x*(x-4)-3*(x-4)+1*(x^2-16) = 0

2*x^2+x^2-11*x-16+12 = 0

3*x^2-11*x-4 = 0

3*x^2-11*x-4 = 0

3*x^2-11*x-4 = 0

DELTA = (-11)^2-(-4*3*4)

DELTA = 169

DELTA > 0

x = (169^(1/2)+11)/(2*3) or x = (11-169^(1/2))/(2*3)

x = 4 or x = -1/3

(x+1/3)*(x-4) = 0

((x+1/3)*(x-4))/((x^2-16)*(x-4)) = 0

((x+1/3)*(x-4))/((x^2-16)*(x-4)) = 0 // * (x^2-16)*(x-4)

(x+1/3)*(x-4) = 0

( x+1/3 )

x+1/3 = 0 // - 1/3

x = -1/3

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4} 

x = -1/3

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