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

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Solution for 5/x-1+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)

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

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

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

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

t_1 = x^-1

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

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

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

DELTA = 65

DELTA > 0

t_1 = (65^(1/2)-7)/(-4*2) or t_1 = (-65^(1/2)-7)/(-4*2)

t_1 = (65^(1/2)-7)/(-8) or t_1 = (65^(1/2)+7)/8

t_1 = (65^(1/2)-7)/(-8)

x^-1-((65^(1/2)-7)/(-8)) = 0

1*x^-1 = (65^(1/2)-7)/(-8) // : 1

x^-1 = (65^(1/2)-7)/(-8)

-1 < 0

1/(x^1) = (65^(1/2)-7)/(-8) // * x^1

1 = ((65^(1/2)-7)/(-8))*x^1 // : (65^(1/2)-7)/(-8)

-8*(65^(1/2)-7)^-1 = x^1

x = -8*(65^(1/2)-7)^-1

t_1 = (65^(1/2)+7)/8

x^-1-((65^(1/2)+7)/8) = 0

1*x^-1 = (65^(1/2)+7)/8 // : 1

x^-1 = (65^(1/2)+7)/8

-1 < 0

1/(x^1) = (65^(1/2)+7)/8 // * x^1

1 = ((65^(1/2)+7)/8)*x^1 // : (65^(1/2)+7)/8

8*(65^(1/2)+7)^-1 = x^1

x = 8*(65^(1/2)+7)^-1

x in { -8*(65^(1/2)-7)^-1, 8*(65^(1/2)+7)^-1 }

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