公告化簡一問

1.若a=1/x ,b=1/y ,求(a-b)/(1/a-1/b)
(a-b)/(1/a-1/b)
=(a-b)/[(b-a)/ab]
= - ab
= - (1/x)(1/y)
= -1/xy

2.若x=a/(a+1) , y=2a/(a-2) ,求(x+y)/3y
(x+y)/3y
={[a/(a+1)]+[2a/(a-2)]}/{3[2a/(a-2)]}
={[a(a-2)+2a(a+1)]/[(a+1)(a-2)]}/[6a/(a-2)]
={[a(a-2)+2a(a+1)]/[(a+1)]}/[6a]
=[a2-2a+2a2+2a]/[6a(a+1)]
=[3a2]/[6a(a+1)]
=a / [2(a+1)]