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

Solution for y=x^2/(x^2-1) equation:

D( x )

x^2-1 = 0

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in (-oo:-1) U (-1:1) U (1:+oo)

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

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

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

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

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

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

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

x^2*y-y = 0

DELTA = 0^2-(4*y*(-y))

DELTA = 4*y^2

4*y^2 = 0

4*y^2 = 0 // : 4

y^2 = 0

y = 0

DELTA = 0  <=>  t_1 = 0

x = 0/(2*y) i y = 0

x = 0 i y = 0

( x = ((4*y^2)^(1/2)+0)/(2*y) or x = (0-(4*y^2)^(1/2))/(2*y) ) i y > 0

( x = 1 or x = -1 ) i y > 0

y+0 > 0

y > 0

y+0 > 0 // - 0

y > 0

x*(x-1)*(x+1) = 0

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

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

x*(x-1)*(x+1) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-1 )

x-1 = 0 // + 1

x = 1

( x )

x = 0

x in { -1} 

x in { 1} 

x = 0