If `1/(x+1)+2/(y+2)+2006/(z+2006)=1` , then the value of `(x^2)/(x^2+x)+(y^2)/(y^2+2y)+(z^2)/(z^2+2006 z)=`

If x/2+2/y=1 and y/2+2/z=1 , then the value of z/2+2/x is:

If x^(2)=y+z,y^(2)=z+x,z^(2)=x+y, then the value of (1)/(x+1)+(1)/(y+1)+(1)/(z+1)

If x + y + z = xyz, then prove that (2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2)) .

If x,y,z are distinct real numbers then the value of ((1)/(x-y))^(2)+((1)/(y-z))^(2)+((1)/(z-x))^(2) is