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

Answer 2

化简得到 (x+y+2)^2除以(x+y+xy+1)后减掉2
所以结果为 -2

Answer 3

(x+y+2)^2除以(x+y+xy+1)后减掉2
结果为 -2

Answer 4

(y+1)/(x+1)+(x+1)/(y+1)
=[(x+1)^2+(y+1)^2]/(x+1)(y+1)
=(x^2+2x+1+y^2+2y+1)/(xy+x+y+1)
=(x^2+y^2+2x+2y+2)/(xy+x+y+1)
=(x^2+2xy+y^2+4x+4y+4)/(xy+x+y+1)-2
=((x+y)^2+2*2(x+y)+2^2)/(xy+x+y+1)-2
=(x+y+2)^2/(xy+x+y+1)-2
=-2（因为x+y+2=0）