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

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Solution for 5/(x^2-4)+2/x=2/(x-2) equation: 


D( x )

x-2 = 0

x = 0

x^2-4 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

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 (-2:0) U (0:2) U (2:+oo)

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

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

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

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

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

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

2*x^3-2*x^3+5*x^2-4*x^2-2*x-8*x+16 = 0

x^2-10*x+16 = 0

x^2-10*x+16 = 0

x^2-10*x+16 = 0

DELTA = (-10)^2-(1*4*16)

DELTA = 36

DELTA > 0

x = (36^(1/2)+10)/(1*2) or x = (10-36^(1/2))/(1*2)

x = 8 or x = 2

(x-2)*(x-8) = 0

((x-2)*(x-8))/(x*(x^2-4)*(x-2)) = 0

((x-2)*(x-8))/(x*(x^2-4)*(x-2)) = 0 // * x*(x^2-4)*(x-2)

(x-2)*(x-8) = 0

( x-2 )

x-2 = 0 // + 2

x = 2

( x-8 )

x-8 = 0 // + 8

x = 8

x in { 2} 

x = 8

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