設xy不等於0 且xy=y-x 則y/x+x/y-xy=? 求過程 不要只留答案就走了.... 然後就不管了...?

Sol
xy<>0
x<>0，y<>0
xy=y－x
xy+x=y
x(y+1)=y
x=y/(y+1)
y/x+x/y-xy
=y/[y/{y+1}]+[y/(y+1)]/y－[y/(y+1)]*y
=(y+1)+[1/(y+1)]－y^2/(y+1)
=[(y+1)^2+1－y^2]/(y+1)
=(y^2+2y+1+1－y^2)/(1+y)
=(2y+2)/(1+y)
=2

Sol
y/x－x/y－xy
=y/x－x/y－y+x
=(y/x－y)－(x－x/y)
=(y/x－xy/x)-[xy/y－x/y]
=(y－xy)/x－(xy－x)/y
=(y－y+x)/x－(y－x－x)/y
=1+1
=2



當x=2時
2y=y－2
y=－2
y/x+x/y－xy
=(－2)/2+2/(－2)－2*(－2)
=－1－1+4
=2
xy=2*(－2)=－4
2xy=－8
都不可能是解答