一道分式求值题已知XY=-12X+Y=-4求(X+1/Y+1)+(Y+1/X+1),

Question

一道分式求值题
已知XY=-12 X+Y=-4
求(X+1/Y+1) + (Y+1/X+1),

Answer 1

(y+1/x+1)+(x+1/y+1)
=[（y+1)^2+(x+1)^2]/[(x+1)+(y+1)]
=[(x^2+y^2)+2(x+y)+2]/[xy+(x+y)+1]
=[（x+y)^2-2xy+2(x+y)+2]/[xy+(x+y)+1] (因为这里x^2+y^2是等于（x+y)^2-2xy的）
代入x+y=-4,xy=-12,得：
原式=[（-4）^2-2×(-12)+2(-4)+2]/[(-12)+(-4)+1]
=(16+24-8+2)/(-12-4+1)
=34/(-15)
=-34/15