2/x-1=4/x^2-1

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Solution for 2/x-1=4/x^2-1 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-1 = 4/(x^2)-1 // - 4/(x^2)-1

2/x-(4/(x^2))-1+1 = 0

2/x-4*x^-2-1+1 = 0

2*x^-1-4*x^-2 = 0

t_1 = x^-1

2*t_1^1-4*t_1^2 = 0

2*t_1-4*t_1^2 = 0

DELTA = 2^2-(-4*0*4)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)-2)/(-4*2) or t_1 = (-4^(1/2)-2)/(-4*2)

t_1 = 0 or t_1 = 1/2

t_1 = 0

x^-1+0 = 0

x^-1 = 0

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

x^-1 = 0

x należy do O

t_1 = 1/2

x^-1-1/2 = 0

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

x^-1 = 1/2

-1 < 0

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

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

2 = x^1

x = 2

x = 2

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