y=3/x2-9

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Solution for y=3/x2-9 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 = 3/(x^2)-9 // - 3/(x^2)-9

y-(3/(x^2))+9 = 0

y-3*x^-2+9 = 0

-3*x^-2 = -(y+9) // : -3

x^-2 = (y+9)/3

-2 < 0

1/(x^2) = (y+9)/3 // * x^2

1 = x^2*((y+9)/3) // : (y+9)/3

3*(y+9)^-1 = x^2

x^2 = 3*(y+9)^-1 // ^ 1/2

abs(x) = 3^(1/2)*(y+9)^(-1/2)

x = 3^(1/2)*(y+9)^(-1/2) or x = -(3^(1/2)*(y+9)^(-1/2))

x in { 3^(1/2)*(y+9)^(-1/2), -(3^(1/2)*(y+9)^(-1/2)) }

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