X/x=x/9

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Solution for X/x=x/9 equation: 


D( x )

x = 0

x = 0

x = 0

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

X/x = x/9 // - x/9

X/x-(x/9) = 0

X*x^-1-1/9*x = 0

t_1 = x^-1

X*t_1^1-1/9*t_1^-1 = 0

X*t_1-1/9*t_1^-1 = 0

t_1^-1*(X*t_1^2-1/9) = 0

X*t_1^2 = 1/9 // : X

t_1^2 = 1/9/X

t_1^2 = 1/9/X // ^ 1/2

abs(t_1) = 1/3/(X^(1/2))

t_1 = 1/3/(X^(1/2)) or t_1 = -(1/3/(X^(1/2)))

1/t_1 = 0

1*t_1^-1 = 0 // : 1

t_1^-1 = 0

t_1 należy do O

t_1 = 1/3/(X^(1/2))

x^-1-(1/3/(X^(1/2))) = 0

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

1*x^-1 = -(-1/3*X^(-1/2)) // : 1

x^-1 = 1/3*X^(-1/2)

-1 < 0

1/(x^1) = 1/3*X^(-1/2) // * x^1

1 = 1/3*X^(-1/2)*x^1 // : 1/3*X^(-1/2)

3*X^(1/2) = x^1

x = 3*X^(1/2)

t_1 = -(1/3/(X^(1/2)))

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

1*x^-1 = -(1/3*X^(-1/2)) // : 1

x^-1 = -1/3*X^(-1/2)

-1 < 0

1/(x^1) = -1/3*X^(-1/2) // * x^1

1 = -1/3*X^(-1/2)*x^1 // : -1/3*X^(-1/2)

-3*X^(1/2) = x^1

x = -3*X^(1/2)

x in { 3*X^(1/2), -3*X^(1/2) }

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