(10/x+2)-1=(9/x^2-4)

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Solution for (10/x+2)-1=(9/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)

10/x-1+2 = 9/(x^2)-4 // - 9/(x^2)-4

10/x-(9/(x^2))-1+2+4 = 0

10/x-9*x^-2-1+2+4 = 0

10*x^-1-9*x^-2+5 = 0

t_1 = x^-1

10*t_1^1-9*t_1^2+5 = 0

10*t_1-9*t_1^2+5 = 0

DELTA = 10^2-(-9*4*5)

DELTA = 280

DELTA > 0

t_1 = (280^(1/2)-10)/(-9*2) or t_1 = (-280^(1/2)-10)/(-9*2)

t_1 = (2*70^(1/2)-10)/(-18) or t_1 = (-2*70^(1/2)-10)/(-18)

t_1 = (2*70^(1/2)-10)/(-18)

x^-1-((2*70^(1/2)-10)/(-18)) = 0

1*x^-1 = (2*70^(1/2)-10)/(-18) // : 1

x^-1 = (2*70^(1/2)-10)/(-18)

-1 < 0

1/(x^1) = (2*70^(1/2)-10)/(-18) // * x^1

1 = ((2*70^(1/2)-10)/(-18))*x^1 // : (2*70^(1/2)-10)/(-18)

-18*(2*70^(1/2)-10)^-1 = x^1

x = -18*(2*70^(1/2)-10)^-1

t_1 = (-2*70^(1/2)-10)/(-18)

x^-1-((-2*70^(1/2)-10)/(-18)) = 0

1*x^-1 = (-2*70^(1/2)-10)/(-18) // : 1

x^-1 = (-2*70^(1/2)-10)/(-18)

-1 < 0

1/(x^1) = (-2*70^(1/2)-10)/(-18) // * x^1

1 = ((-2*70^(1/2)-10)/(-18))*x^1 // : (-2*70^(1/2)-10)/(-18)

-18*(-2*70^(1/2)-10)^-1 = x^1

x = -18*(-2*70^(1/2)-10)^-1

x in { -18*(2*70^(1/2)-10)^-1, -18*(-2*70^(1/2)-10)^-1 }

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