Let, a^(1/2)=x. :. a^(3/2)=x^3.
:. (1-a^(3/2))/(1-a^(1/2)),
=(1-x^3)/(1-x),
={cancel((1-x))(1+x+x^2)}/cancel((1-x)).
:. (1-a^(3/2))/(1-a^(1/2))=(1+x+x^2).
:. (1-a^(3/2))/(1-a^(1/2))+a^(1/2)=(1+x+x^2)+x=1+2x+x^2, or,
(1-a^(3/2))/(1-a^(1/2))+a^(1/2)=(1+x)^2.......(star^1).
On the similar lines, we can have,
(1+a^(3/2))/(1+a^(1/2))-a^(1/2)=(1-x)^2........(star^2).
Combining (star^1) and (star^2), we have,
{((1-a^(3/2))/(1-a^(1/2))+a^(1/2))( (1+a^(3/2))/(1+a^(1/2))-a^(1/2))}=(1-x^2)^2.
Hence, the Exp. =(1-x^4)-:(1-x^2)^2+1,
={(1+x^2)(1-x^2)}-:(1-x^2)^2+1,
=(1+x^2)/(1-x^2)+1,
={(1+x^2)+(1-x^2)}/(1-x^2),
=2/(1-x^2),
=2/(1-a), (a ge 0, a!=1).