分式的加减法：实数x、y满足x^2+y^2+8x+6y+25=0,求x^2-4y^2/x^2+4xy+4y^2-x/x+2y的值._数学解答

分式的加减法：实数x、y满足x^2+y^2+8x+6y+25=0,求x^2-4y^2/x^2+4xy+4y^2-x/x+2y的值.

人气：134 ℃　时间：2019-10-30 03:32:12

解答

x^2+y^2+8x+6y+25 =(x+4)^2+(y+3)^2=0 则x+4=0 y+3=0 (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) =-2y/(x+2y) =6/-10 =-3/5