化簡
(x-y)/(x²-y²)
=(x-y)/(x+y)(x-y)
=1/(x+y)
比較(x+y)/(x²+y²) 和1/(x+y)大小,
[(x+y)/(x²+y²)]÷ [1/(x+y)]
=(x+y)² /(x²+y²)
=(x²+2xy+y²)/(x²+y²)
=1+2xy/(x²+y²)
因為x>0,y>0
所以2xy/(x²+y²)>0
所以1+2xy/(x²+y²) >1
即[(x+y)/(x²+y²)]÷ [1/(x+y)]>1
所以(x+y)/(x²+y²)>1/(x+y)
所以兩人都是錯的,值變小了

x+y分之x的平方+y的平方寫成x-y分之x的平方-y的平方
化簡
(x²-y²)/(x-y)
=(x+y)(x-y)/(x-y)
=x+y
比較(x²+y²)/(x+y) 和x+y大小
(x²+y²)/(x+y) -(x+y)
=(x²+y²)/(x+y) -(x+y)²/(x+y)
=[(x²+y²)-(x+y)²] /(x+y)
=(-2xy)/(x+y)
因為x>0,y>0
所以-2xy0
所以-2xy/(x+y)