Solution:
A term in the expansion of is of the form
This term will be rational if ,and are both rational
numbers. This is possible if and only if r is a multiple of 2
and s is a multiple of 3. Possible values of r are 0, 2, 4 and
6 whereas the possible values of s are 0, 3 and 6. Also note that
For . s can take value 0, 3 or 6.
For s can take value 0 or 3.
For r = 4, s can take value 0.
For r = 6, s can take value 0.
Thus, the number of rational terms is 3 + 2 + 1 + 1 = 7