curve eqn y^2+x^2=4

(i) verify that x=t-t^-1 and y=t+t^-1 are paramtrics of that curve (DONE)

(ii) show that dy/dx=((t-1)(t+1))/(t^2+1) in this form

i did dy/dx=dy/dt x dt/dx

= (1-t^-2)(1+t^2) i get stuck here getting into required form.

or do 2ydy/dx + 2x = 0

get: dy/dx = (t-t^-1)/(t+t^-1) stuck again

im sure im just partially being stupid,, if n e one can spot how to factorise for me that'd be gr8 cheers