Question

初二分式的加减法题

若x+y=4，xy=-12，求代数式（y+1）/（x+1）+（x+1）/（y+1）的值

/代表除号

谢谢！

Answer 1

（y+1）/（x+1）+（x+1）/（y+1）
=[(Y+1)方+(X+1)方]/[(X+1)(Y+1)]
=(Y方+2Y+1+X方+2X+1)/(XY+X+Y+1)
=[(X方+Y方)+2*4+2]/(-12+4+1)
=[(X+Y)方-2XY+10)/(-7)
=(16+24+10)/(-7)
=-50/7

Answer 2

由x+y=4，xy=-12得出
x=6，y=-2，代入（y+1）/（x+1）+（x+1）/（y+1）
得出-50/7

Answer 3

解：原式=[(y+1)^2+(x+1)^2]/[(x+1)(y+1)]
=(x^2+y^2+2x+2y+2)/(x+y+xy+1)
=(x^2+y^2+2x+2y+2)/(4-12+1)
=(x^2+y^2+2xy-2xy+2x+2y+2)/(-7)
=[(x+y)^2-2xy+2(x+y)+2]/(-7)
=(16+24+8+2)/(-7)
=-50/7