已知x+y=2,xy=-15,求（y+1)÷(x+1)+(X+1)÷(y+1)的值

已知x+y=2,xy=-15,求（y+1)÷(x+1)+(X+1)÷(y+1)的值
已知x+y=2,xy=-15,求（y+1)÷(x+1)+(X+1)÷(y+1)的值

已知x+y=2,xy=-15,求（y+1)÷(x+1)+(X+1)÷(y+1)的值
x²+y²=(x+y)²-2xy=2²-2×(-15)=34
(y+1)/(x+1)+(x+1)/(y+1)
通分得
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
展开得
=[y²+2y+1+x²+2x+1]/(xy+x+y+1)
=[(x²+y²)+2(x+y)+2]/[xy+(x+y)+1]
代入已知量
=(34+2×2+2)/(-15+2+1)
=40/(-12)
=-10/3

x=3 y=-5或x=-3 y=5 结果-10/3

-10/3
通分后，分母裂项得到xy+x+y+1,分子裂项后+2xy-2xy再合并得到（x+y）的平方+2(x+y)-2xy+2,计算得出-10/3