(9-1/x^2)/(3+1/x)

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Solution for (9-1/x^2)/(3+1/x) equation: 


D( x )

x = 0

1/x+3 = 0

x^2 = 0

x = 0

x = 0

1/x+3 = 0

1/x+3 = 0

1*x^-1 = -3 // : 1

x^-1 = -3

-1 < 0

1/(x^1) = -3 // * x^1

1 = -3*x^1 // : -3

-1/3 = x^1

x = -1/3

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:-1/3) U (-1/3:0) U (0:+oo)

(9-(1/(x^2)))/(1/x+3) = 0

(9-x^-2)/(1/x+3) = 0

(9-x^-2)/(x^-1+3) = 0

-1*x^-2 = -9 // : -1

x^-2 = 9

-2 < 0

1/(x^2) = 9 // * x^2

1 = 9*x^2 // : 9

1/9 = x^2

x^2 = 1/9 // ^ 1/2

abs(x) = 1/3

x = 1/3 or x = -1/3

x in { -1/3} 

x = 1/3

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