（4/x²-y²+x+y/xy²-x²y）÷（x+2y）（x-y）/x²y+2xy²,其中x=-1,y=-3...

（4/x²-y²+x+y/xy²-x²y）÷（x+2y）（x-y）/x²y+2xy²,其中x=-1,y=-3...
（4/x²-y²+x+y/xy²-x²y）÷（x+2y）（x-y）/x²y+2xy²,其中x=-1,y=-3.
..

（4/x²-y²+x+y/xy²-x²y）÷（x+2y）（x-y）/x²y+2xy²,其中x=-1,y=-3...
原式=[4/（x+y)(x-y)-(x+y)/xy(x-y)]÷【（x+2y)(x-y)/xy(x+2y)]
=[4xy-(x+y)^2]/xy(x+y)(x-Y)*[xy/(x-y)]
=[-(x-y)^2]/xy(x+y)(x-y)*[xy/(x-y)]
=-1/(x+y)
当x=-1,y=-3时,原式=-1/(-1-3)=1/4

原式=[4/(x+y)(x-y)+(x+y)/xy(y-x)]÷[(x+2y)(x-y)/xy(x+2y)]
=[-4xy/xy(x+y)(y-x)+(x+y)(x+y)/xy(x+y)(y-x)]÷(x-y)/xy
=[(-4xy+x^2+2xy+y^2)/xy(x+y)(y-x)]*xy/(x-y)
=(x-y)^2/(x+y)(y-x)(x-y)
=-1/(x+y)
将x=-1，y=-3代入上式
原式=1/4