[(1/a+1/b)^2]/(1/a^2-1/b^2)
=[(1/a+1/b)^2]/[(1/a-1/b)(1/a+1/b)]
=(1/a+1/b)/(1/a-1/b)
=[(a+b)/ab]/[(b-a)/ab]
=(a+b)/(b-a)