Question

已知x+y=-2.xy=-10,求y+1除以x+1加x+1除以y+1的值

Answer 1

解题思想：对于分式求值,先通分,然后尽可能将分子分母向已知条件转化,

即全部化成有关x+y与xy,最后将已知值代入求解.

(y+1)/(x+1)+(x+1)/(y+1)

=[(y+1)²+(x+1)²]/[(x+1)(y+1)]

=(x²+y²+2x+2y+2)/(xy+x+y+1)

=[(x+y)²-2xy+2(x+y)+2]/(xy+x+y+1)

=(4+20-4+2)/(-10-2+1)

=22/(-11)

=-2