已知x+y=-4.xy=12,求x+1分之y+1加上y+1分之x+1的值

题目

已知x+y=-4.xy=12,求x+1分之y+1加上y+1分之x+1的值

答案

(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)²-2xy+2(x+y)+2]/(xy+x+y+1)=[(-4)²-2*12+2*(-4)+2]/(12-4+1)=-14/9