(5/x-1)+1=(10/x^2-1)

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Solution for (5/x-1)+1=(10/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-1+1 = 10/(x^2)-1 // - 10/(x^2)-1

5/x-(10/(x^2))-1+1+1 = 0

5/x-10*x^-2-1+1+1 = 0

5*x^-1-10*x^-2+1 = 0

t_1 = x^-1

5*t_1^1-10*t_1^2+1 = 0

5*t_1-10*t_1^2+1 = 0

DELTA = 5^2-(-10*1*4)

DELTA = 65

DELTA > 0

t_1 = (65^(1/2)-5)/(-10*2) or t_1 = (-65^(1/2)-5)/(-10*2)

t_1 = (65^(1/2)-5)/(-20) or t_1 = (65^(1/2)+5)/20

t_1 = (65^(1/2)-5)/(-20)

x^-1-((65^(1/2)-5)/(-20)) = 0

1*x^-1 = (65^(1/2)-5)/(-20) // : 1

x^-1 = (65^(1/2)-5)/(-20)

-1 < 0

1/(x^1) = (65^(1/2)-5)/(-20) // * x^1

1 = ((65^(1/2)-5)/(-20))*x^1 // : (65^(1/2)-5)/(-20)

-20*(65^(1/2)-5)^-1 = x^1

x = -20*(65^(1/2)-5)^-1

t_1 = (65^(1/2)+5)/20

x^-1-((65^(1/2)+5)/20) = 0

1*x^-1 = (65^(1/2)+5)/20 // : 1

x^-1 = (65^(1/2)+5)/20

-1 < 0

1/(x^1) = (65^(1/2)+5)/20 // * x^1

1 = ((65^(1/2)+5)/20)*x^1 // : (65^(1/2)+5)/20

20*(65^(1/2)+5)^-1 = x^1

x = 20*(65^(1/2)+5)^-1

x in { -20*(65^(1/2)-5)^-1, 20*(65^(1/2)+5)^-1 }

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