已知x+y=-2,xy=-1求(y+1)/(x+1)+(x+1)/(y+1)的值
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解:
原式
=(y+1)/(x+1)+(x+1)/(y+1)
=[(y+1)^2]/[(x+1)(y+1)]+[(x+1)^2]/[(x+1)(y+1)]
=[(y+1)^2+(x+1)^2]/[(x+1)(y+1)]
=[y^2+2y+1+x^2+2x+1]/[xy+x+y+1]
=[(x^2+y^2)+2(x+y)+2]/[(x+y)+xy+1]
=[(x^2+y^2+2xy)-2xy+2(x+y)+2]/[(x+y)+xy+1]
=[(x+y)^2-2xy+2(x+y)+2]/[(x+y)+xy+1]
由于：x+y=-2,xy=-1
则：原式
=[(-2)^2-2(-1)+2(-2)+2]/[(-2)+(-1)+1]
=4/(-2)
=-2
原式
=(y+1)/(x+1)+(x+1)/(y+1)
=[(y+1)^2]/[(x+1)(y+1)]+[(x+1)^2]/[(x+1)(y+1)]
=[(y+1)^2+(x+1)^2]/[(x+1)(y+1)]
=[y^2+2y+1+x^2+2x+1]/[xy+x+y+1]
=[(x^2+y^2)+2(x+y)+2]/[(x+y)+xy+1]
=[(x^2+y^2+2xy)-2xy+2(x+y)+2]/[(x+y)+xy+1]
=[(x+y)^2-2xy+2(x+y)+2]/[(x+y)+xy+1]
由于：x+y=-2,xy=-1
则：原式
=[(-2)^2-2(-1)+2(-2)+2]/[(-2)+(-1)+1]
=4/(-2)
=-2
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