a/x-b/x^2

Solution for a/x-b/x^2 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)

a/x-(b/(x^2)) = 0

a*x^-1-(b*x^-2) = 0

t_1 = x^-1

a*t_1^1-b*t_1^2 = 0

a*t_1-b*t_1^2 = 0

DELTA = a^2-(0*4*(-b))

DELTA = a^2

a^2 = 0

1*a^2 = 0 // : 1

a^2 = 0

a = 0

DELTA = 0  <=>  t_2 = 0

t_1 = -a/(2*(-b)) i a = 0

t_1 = (1/2)*a*b^-1 i a = 0

( t_1 = ((a^2)^(1/2)-a)/(2*(-b)) or t_1 = (-a-(a^2)^(1/2))/(2*(-b)) ) i a > 0

( t_1 = 0 or t_1 = a*b^-1 ) i a > 0

a+0 > 0

a > 0

a+0 > 0 // - 0

a > 0

t_1 = (1/2)*a*b^-1

x^-1-((1/2)*a*b^-1) = 0

(-1/2)*a*b^-1+x^-1 = 0

1*x^-1 = -(-1/2*a*b^-1) // : 1

x^-1 = 1/2*a*b^-1

-1 < 0

1/(x^1) = 1/2*a*b^-1 // * x^1

1 = 1/2*a*b^-1*x^1 // : 1/2*a*b^-1

2*a^-1*b = x^1

x = 2*a^-1*b

t_1 = 0

x^-1+0 = 0

x^-1 = 0

1*x^-1 = 0 // : 1

x^-1 = 0

x naleu017Cy do O

t_1 = a*b^-1

x^-1-(a*b^-1) = 0

1*x^-1 = a*b^-1 // : 1

x^-1 = a*b^-1

-1 < 0

1/(x^1) = a*b^-1 // * x^1

1 = a*b^-1*x^1 // : a*b^-1

1/(a*b^-1) = x^1

x = 1/(a*b^-1)

x in { 2*a^-1*b, 1/(a*b^-1) }