If a - 1/(a - 3) = 3 Then find , (a - 3)3 - 1/((a - 3)^3)

Given = a - \(\frac{1}{a - 3}\) = 3

By subtracting 3 on both sides we get,

(a - 3) - \(\frac{1}{a - 3}\) = 3 - 3 = 0

(a - 3)³ - \(\frac{1}{(a - 3)^3}\) = 0³ + 3 × 0 = 0

 

Note - if x -  \(\frac{1}{x}\) = a

then x³ - \(\frac{1}{x^3}\) =  a³ + 3a