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)#.
