正数A，B满足A*A-B*B=2AB，求（A-B）/（A+B）

B/A
A*A-B*B=2AB可推出A*A-AB=B*B+AB
即A（A-B）=B（A+ B）
因为正数A，B
（A-B）/（A+B）=B/A

A*A-B*B=2AB
所以A*A=B*B+2AB

（A-B）/（A+B)
=[（A-B）*（A-B)]/[（A+B)（A-B)]

=[A*A+B*B-2AB]/[A*A-B*B]
=[A*A+B*B-2AB]/2AB
=[A*A+B*B]/2AB - 1
=[B*B+2AB]/2AB -1
=B*B/2AB +1-1
=B/2A

(A-B)/(A+B)=[(A+B)(A-B)]/[(A+B)(A+B)]
=(A^2-B^2)/(A^2+B^2+2AB)
=2AB/(A^2+B^2+A^2-B^2)
=2AB/(2A^2)
=B/A