2/x^2+1=x^2

Solution for 2/x^2+1=x^2 equation:

D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

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

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

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

t_1 = x^2

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

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

(1*t_1^1-1*t_1^2+2*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^1-1*t_1^2+2*t_1^0) = 0

t_1^1

t_1-t_1^2+2 = 0

t_1-t_1^2+2 = 0

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

DELTA = 9

DELTA > 0

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

t_1 = -1 or t_1 = 2

t_1 in { -1, 2} 

t_1 = -1

x^2+1 = 0

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

x^2 = -1

t_1 = 2

x^2-2 = 0

1*x^2 = 2 // : 1

x^2 = 2

x^2 = 2 // ^ 1/2

abs(x) = 2^(1/2)

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

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