(2/x-1)+(5/x+1)=(3/x^2-1)

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Solution for (2/x-1)+(5/x+1)=(3/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+5/x-1+1 = 3/(x^2)-1 // - 3/(x^2)-1

2/x+5/x-(3/(x^2))-1+1+1 = 0

2/x+5/x-3*x^-2-1+1+1 = 0

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

t_1 = x^-1

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

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

DELTA = 7^2-(-3*1*4)

DELTA = 61

DELTA > 0

t_1 = (61^(1/2)-7)/(-3*2) or t_1 = (-61^(1/2)-7)/(-3*2)

t_1 = (61^(1/2)-7)/(-6) or t_1 = (61^(1/2)+7)/6

t_1 = (61^(1/2)-7)/(-6)

x^-1-((61^(1/2)-7)/(-6)) = 0

1*x^-1 = (61^(1/2)-7)/(-6) // : 1

x^-1 = (61^(1/2)-7)/(-6)

-1 < 0

1/(x^1) = (61^(1/2)-7)/(-6) // * x^1

1 = ((61^(1/2)-7)/(-6))*x^1 // : (61^(1/2)-7)/(-6)

-6*(61^(1/2)-7)^-1 = x^1

x = -6*(61^(1/2)-7)^-1

t_1 = (61^(1/2)+7)/6

x^-1-((61^(1/2)+7)/6) = 0

1*x^-1 = (61^(1/2)+7)/6 // : 1

x^-1 = (61^(1/2)+7)/6

-1 < 0

1/(x^1) = (61^(1/2)+7)/6 // * x^1

1 = ((61^(1/2)+7)/6)*x^1 // : (61^(1/2)+7)/6

6*(61^(1/2)+7)^-1 = x^1

x = 6*(61^(1/2)+7)^-1

x in { -6*(61^(1/2)-7)^-1, 6*(61^(1/2)+7)^-1 }

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