y=5/x^2-1

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Solution for y=5/x^2-1 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

y = 5/(x^2)-1 // - 5/(x^2)-1

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

y-5*x^-2+1 = 0

-5*x^-2 = -(y+1) // : -5

x^-2 = (y+1)/5

-2 < 0

1/(x^2) = (y+1)/5 // * x^2

1 = x^2*((y+1)/5) // : (y+1)/5

5*(y+1)^-1 = x^2

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

abs(x) = 5^(1/2)*(y+1)^(-1/2)

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

x in { 5^(1/2)*(y+1)^(-1/2), -(5^(1/2)*(y+1)^(-1/2)) }

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