If a = 1/(a -5), where a ≠ 5 and a ≠ 0, find the values of: (i) (a - 1/a) (ii) (a + 1/a) (iii) (a² - 1/a²) (iv) (a² + 1/a²)

(i) Given, Hence, (ii) From part (i), Using identity, Hence, (iii) From (i) and (ii), Using identity, Hence, (iv) From (i) and (ii), Using identity, Hence, .