y=1/x^2+2x-3

Solution for y=1/x^2+2x-3 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)

y = 2*x+1/(x^2)-3 // - 2*x+1/(x^2)-3

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

y-2*x-x^-2+3 = 0

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

(3*x^2-2*x^3-1*x^0)/(x^2) = 0 // * x^4

x^2*(3*x^2-2*x^3-1*x^0) = 0

x^2

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

{ 1, -1 }

1

x = 1

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

1

x-1

x-2*x^2+1

3*x^2-2*x^3-1

x-1

2*x^3-2*x^2

x^2-1

x-x^2

x-1

1-x

0

x-2*x^2+1 = 0

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

DELTA = 9

DELTA > 0

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

x = -1/2 or x = 1

x in { -1/2, 1, 1} 

x in { -1/2, 1, 1 }