(6/x^2-9)-(1/x-3)=1

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Solution for (6/x^2-9)-(1/x-3)=1 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

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

6*x^-2-x^-1-7 = 0

t_1 = x^-1

6*t_1^2-1*t_1^1-7 = 0

6*t_1^2-t_1-7 = 0

DELTA = (-1)^2-(-7*4*6)

DELTA = 169

DELTA > 0

t_1 = (169^(1/2)+1)/(2*6) or t_1 = (1-169^(1/2))/(2*6)

t_1 = 7/6 or t_1 = -1

t_1 = -1

x^-1+1 = 0

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

x^-1 = -1

-1 < 0

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

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

-1 = x^1

x = -1

t_1 = 7/6

x^-1-7/6 = 0

1*x^-1 = 7/6 // : 1

x^-1 = 7/6

-1 < 0

1/(x^1) = 7/6 // * x^1

1 = 7/6*x^1 // : 7/6

6/7 = x^1

x = 6/7

x in { -1, 6/7 }

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