2009/028) Rationalize the denominator of expression? [1 / {1 + x^1/5}]

Rationalize the denominator of expression?
[1 / {1 + x^1/5}]


ANS:
we know that (x^(1/5))^5 = x

say x^(1/5) = a

1+ x^ 1/5 = (1+ a)

as (1+a^5)/(1+a) = (1-a+a^2-a^3+a^4) and 1+a^5 in terms of x is rationalised

so
[1 / {1 + x^1/5}] = (1-x^(1/5) + x^(2/5) - x(^3/5) + x^(4/5))/(1+x)