(6)/(x^2-2x)=(1)/(x^2-4)

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Solution for (6)/(x^2-2x)=(1)/(x^2-4) equation: 


D( x )

x^2-(2*x) = 0

x^2-4 = 0

x^2-(2*x) = 0

x^2-(2*x) = 0

x^2-2*x = 0

x^2-2*x = 0

DELTA = (-2)^2-(0*1*4)

DELTA = 4

DELTA > 0

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

x = 2 or 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)

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

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

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

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

x^2-2*x = 0

x^2-2*x = 0

x*(x-2) = 0

x-2 = 0 // + 2

x = 2

x*(x-2) = 0

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

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

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

5*x^2+2*x-24 = 0

5*x^2+2*x-24 = 0

5*x^2+2*x-24 = 0

DELTA = 2^2-(-24*4*5)

DELTA = 484

DELTA > 0

x = (484^(1/2)-2)/(2*5) or x = (-484^(1/2)-2)/(2*5)

x = 2 or x = -12/5

(x+12/5)*(x-2) = 0

((x+12/5)*(x-2))/(x*(x-2)*(x^2-4)) = 0

((x+12/5)*(x-2))/(x*(x-2)*(x^2-4)) = 0 // * x*(x-2)*(x^2-4)

(x+12/5)*(x-2) = 0

( x+12/5 )

x+12/5 = 0 // - 12/5

x = -12/5

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = -12/5

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