`((x^(- 1)+y^(- 1))/(x^(- 1)))^(- 1)+((x^(- 1)-y^(- 1))/(x^(- 1)))^(- 1)=(2y^2)/(y^2-x^2)` Prove that

Prove that ((x^(-1)+y^(-1))/x^(-1))^(-1)+((x^(-1)-y^(-1))/x^(-1))^(-1)=(2y^(2))/(y^(2)-x^(2))

Prove that ((x^(-1)+y^(-1)))/(x^(-1))+((x^(-1)+y^(-1)))/(y^(-1))=(x+y)^2/(xy)

If y=(x^(2)+x+1)/(x^(2)-x+1)," then "(x^(2)-x+1)^(2)y_(1)=

If y=(cot^(-1)x)^(2), prove that y_(2)(x^(2)+1)^(2)+2x(x^(2)+1)y_(1)=2

If y=(cot^(-1)x)^(2), prove that y_(2)(x^(2)+1)^(2)+2x(x^(2)+1)y_(1)=2

If y=x+(1)/(x+(1)/(x+(1)/(x+1))), prove that (dy)/(dx)=(y)/(2y-x)

If y=x+(1)/(x+(1)/(x+(1)/(x+))), prove that (dy)/(dx)=(y)/(2y-x)

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

If y=x+(1)/(x+(1)/((1)/(x+...))), prove that(dy)/(dx)=(y)/(2y-x)