(4/x+1+2/x-1)=35/x^2-1

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Solution for (4/x+1+2/x-1)=35/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)

4/x+2/x-1+1 = 35/(x^2)-1 // - 35/(x^2)-1

4/x+2/x-(35/(x^2))-1+1+1 = 0

4/x+2/x-35*x^-2-1+1+1 = 0

6*x^-1-35*x^-2+1 = 0

t_1 = x^-1

6*t_1^1-35*t_1^2+1 = 0

6*t_1-35*t_1^2+1 = 0

DELTA = 6^2-(-35*1*4)

DELTA = 176

DELTA > 0

t_1 = (176^(1/2)-6)/(-35*2) or t_1 = (-176^(1/2)-6)/(-35*2)

t_1 = (4*11^(1/2)-6)/(-70) or t_1 = (-4*11^(1/2)-6)/(-70)

t_1 = (4*11^(1/2)-6)/(-70)

x^-1-((4*11^(1/2)-6)/(-70)) = 0

1*x^-1 = (4*11^(1/2)-6)/(-70) // : 1

x^-1 = (4*11^(1/2)-6)/(-70)

-1 < 0

1/(x^1) = (4*11^(1/2)-6)/(-70) // * x^1

1 = ((4*11^(1/2)-6)/(-70))*x^1 // : (4*11^(1/2)-6)/(-70)

-70*(4*11^(1/2)-6)^-1 = x^1

x = -70*(4*11^(1/2)-6)^-1

t_1 = (-4*11^(1/2)-6)/(-70)

x^-1-((-4*11^(1/2)-6)/(-70)) = 0

1*x^-1 = (-4*11^(1/2)-6)/(-70) // : 1

x^-1 = (-4*11^(1/2)-6)/(-70)

-1 < 0

1/(x^1) = (-4*11^(1/2)-6)/(-70) // * x^1

1 = ((-4*11^(1/2)-6)/(-70))*x^1 // : (-4*11^(1/2)-6)/(-70)

-70*(-4*11^(1/2)-6)^-1 = x^1

x = -70*(-4*11^(1/2)-6)^-1

x in { -70*(4*11^(1/2)-6)^-1, -70*(-4*11^(1/2)-6)^-1 }

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