X2+Y2+8X+6Y+25=0 求代数式(x2-4y2/x2+4xy+4y2)-x/x+2y

题目

X2+Y2+8X+6Y+25=0 求代数式(x2-4y2/x2+4xy+4y2)-x/x+2y

答案

X2+Y2+8X+6Y+25=0
x^2+y^2+8x+6y+25=0
x^2+8x+16+y^2+6y+9=0
(X+4)^2+(y+3)^2=0
x=-4 y=-3
（x^2-4y^2)/(x^2+4xy+4y^2)-x/x+2y
=(x-2y)(x+2y)/(x+2y)^2-x/x+2y
=(x-2y)/(X+2y)-x/x+2y
=(x-2y-x)/x+2y
=-2y/x+2y
=-2(-3)/(-4)+2(-3)
=6/-10
=-3/5