factor
((r/s + s/r)) / ((r^2/s^2 - s^2/r^2))
=[ (r^2 + s^2)/(rs) ] / [ (r^4 - s^4)/(r^2s^2) ]
= (r^2 + s^2)/(rs) [(r^2s^2)/((r^2+s^2)(r^2-s^2))
= rs/(r^2-s^2)
((r/s + s/r)) / ((r^2/s^2 - s^2/r^2))
= (r^2 + s^2)/(rs) [(r^2s^2)/((r^2+s^2)(r^2-s^2))
= rs/(r^2-s^2)