已知x+y=-4，xy=-12，求y+1x+1+x+1y+1

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原式=(y+1)
======以下答案可供参考======
供参考答案1:
y+1/x+1+x+1/y+1
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
=[x²+y²+2(x+y)+2]/(x+y+xy+1)
=[(x+y)²+2(x+y)-2xy+2]/(x+y+xy+1)
=[(-4)²+2x(-4)-2x(-12)+2]/(-4-12+1)=-34/15
供参考答案2:
y+1/x+1+x+1/y+1
=(y+1)²+（x+1)²/(x+1)(y+1)
=y²+2y+1+x²+2x+1/xy+x+y+1
=(x+y)²+2(x+y)+2-2xy/xy+x+y+1
把x+y=-4 xy=-12 代入上式
解得：y+1/x+1+x+1/y+1= ﹣34/15
采纳吧 亲 这么晚写滴 挺辛苦哦