If a - 1/(a - 2) = 4 Then find , (a - 2)2 + 1/((a - 2)^2)

Given = a - \(\frac{1}{a - 2}\) = 4

By subtracting 2 on both sides we get,

(a - 2) - \(\frac{1}{a - 2}\) = 4 - 2 = 2

(a - 2)² + \(\frac{1}{(a - 2)^2}\) = 2² + 2 = 6

 

If x - \(\frac{1}{x}\) = a

then, x² + \(\frac{1}{x^2}\) = a² + 2