Find dy/dx, when If x = (t + 1/t) and y = a(t - 1/t), prove that dy/dx = x/y

Question

Find \(\cfrac{dy}{d\mathrm x} \), when

If x = (t + \(\cfrac{1}t\)) and y = a(t - \(\cfrac{1}t\)), prove that \(\cfrac{dy}{d\mathrm x} \) = \(\cfrac{\text x}{y}\)

Answer 1

as x = (t + \(\cfrac{1}t\))

Differentiating it with respect to t,

Differentiating it with respect to t,

Dividing equation (2) by (1),