y=8/(x^2-4)

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

D( x )

x^2-4 = 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 (-2:2) U (2:+oo)

y = 8/(x^2-4) // - 8/(x^2-4)

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

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

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

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

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

x^2*y-4*y-8 = 0

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

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

x^2*y-4*y-8 = 0

x^2*y = -(-4*y-8) // : y

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

x^2 = (4*y+8)/y // ^ 1/2

abs(x) = ((4*y+8)^(1/2))/(y^(1/2))

x = ((4*y+8)^(1/2))/(y^(1/2)) or x = -(((4*y+8)^(1/2))/(y^(1/2)))

x in { ((4*y+8)^(1/2))/(y^(1/2)), -(((4*y+8)^(1/2))/(y^(1/2))) }