2/x+2+5/x-2=6/x^2-4

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Solution for 2/x+2+5/x-2=6/x^2-4 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-2+2 = 6/(x^2)-4 // - 6/(x^2)-4

2/x+5/x-(6/(x^2))-2+2+4 = 0

2/x+5/x-6*x^-2-2+2+4 = 0

7*x^-1-6*x^-2+4 = 0

t_1 = x^-1

7*t_1^1-6*t_1^2+4 = 0

7*t_1-6*t_1^2+4 = 0

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

DELTA = 145

DELTA > 0

t_1 = (145^(1/2)-7)/(-6*2) or t_1 = (-145^(1/2)-7)/(-6*2)

t_1 = (145^(1/2)-7)/(-12) or t_1 = (145^(1/2)+7)/12

t_1 = (145^(1/2)-7)/(-12)

x^-1-((145^(1/2)-7)/(-12)) = 0

1*x^-1 = (145^(1/2)-7)/(-12) // : 1

x^-1 = (145^(1/2)-7)/(-12)

-1 < 0

1/(x^1) = (145^(1/2)-7)/(-12) // * x^1

1 = ((145^(1/2)-7)/(-12))*x^1 // : (145^(1/2)-7)/(-12)

-12*(145^(1/2)-7)^-1 = x^1

x = -12*(145^(1/2)-7)^-1

t_1 = (145^(1/2)+7)/12

x^-1-((145^(1/2)+7)/12) = 0

1*x^-1 = (145^(1/2)+7)/12 // : 1

x^-1 = (145^(1/2)+7)/12

-1 < 0

1/(x^1) = (145^(1/2)+7)/12 // * x^1

1 = ((145^(1/2)+7)/12)*x^1 // : (145^(1/2)+7)/12

12*(145^(1/2)+7)^-1 = x^1

x = 12*(145^(1/2)+7)^-1

x in { -12*(145^(1/2)-7)^-1, 12*(145^(1/2)+7)^-1 }

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