3+1/x=10/x^2

Solution for 3+1/x=10/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)

1/x+3 = 10/(x^2) // - 10/(x^2)

1/x-(10/(x^2))+3 = 0

1/x-10*x^-2+3 = 0

x^-1-10*x^-2+3 = 0

t_1 = x^-1

1*t_1^1-10*t_1^2+3 = 0

t_1-10*t_1^2+3 = 0

DELTA = 1^2-(-10*3*4)

DELTA = 121

DELTA > 0

t_1 = (121^(1/2)-1)/(-10*2) or t_1 = (-121^(1/2)-1)/(-10*2)

t_1 = -1/2 or t_1 = 3/5

t_1 = -1/2

x^-1+1/2 = 0

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

x^-1 = -1/2

-1 < 0

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

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

-2 = x^1

x = -2

t_1 = 3/5

x^-1-3/5 = 0

1*x^-1 = 3/5 // : 1

x^-1 = 3/5

-1 < 0

1/(x^1) = 3/5 // * x^1

1 = 3/5*x^1 // : 3/5

5/3 = x^1

x = 5/3

x in { -2, 5/3 }