2/x^2-1-1/x-1=1

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Solution for 2/x^2-1-1/x-1=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)

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

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

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

2*x^-2-x^-1-3 = 0

t_1 = x^-1

2*t_1^2-1*t_1^1-3 = 0

2*t_1^2-t_1-3 = 0

DELTA = (-1)^2-(-3*2*4)

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+1)/(2*2) or t_1 = (1-25^(1/2))/(2*2)

t_1 = 3/2 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 = 3/2

x^-1-3/2 = 0

1*x^-1 = 3/2 // : 1

x^-1 = 3/2

-1 < 0

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

1 = 3/2*x^1 // : 3/2

2/3 = x^1

x = 2/3

x in { -1, 2/3 }

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