((3)/(x-2))-((8)/(x^2-4))

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Solution for ((3)/(x-2))-((8)/(x^2-4)) equation: 


D( x )

x-2 = 0

x^2-4 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

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

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

3/(x-2)-8*(x^2-4)^-1 = 0

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

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

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

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

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

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

DELTA = (-8)^2-(3*4*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)+8)/(2*3) or x = (8-16^(1/2))/(2*3)

x = 2 or x = 2/3

(x-2/3)*(x-2) = 0

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

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

(x-2/3)*(x-2) = 0

( x-2/3 )

x-2/3 = 0 // + 2/3

x = 2/3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = 2/3

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