[(x y)/(x-y) 4xy/(y^2-x^2)]/[（x^2 2xy-3y^2)/(x^2-9y^2)]其中3x^2 xy-2y^2=0

[(x+y)/(x-y)+4xy/(y^2-x^2)]/[（x^2+2xy-3y^2)/(x^2-9y^2)]其中3x^2+xy-2y^2=0

热心网友

分子：(x+y)/(x-y)+4xy/(y^2-x^2) =-(x+y)/(y-x)+4xy/(y^2-x^2) =-(x+y)(y+x)/(y^2-x^2)+4xy/(y^2-x^2) =-[(x^2+2xy+y^2-4xy)/(y^2-x^2)] =-(y-x)^2/(y^2-x^2) =-(y-x)/(y+x) =(x-y)/(x+y)分母：（x^2+2xy-3y^2)/(x^2-9y^2) =(x+3y)(x-y)/(x+3y)(x-3y) =(x-y)/(x-3y)然后分子/分母得(x-3y)/(x+y) ---------------------------表达式（1）由3x^2+xy-2y^2=0得出[x-（2/3）y](x+y)=0得[x-（2/3）y]=0（即x=（2/3）y）或(x+y)=0根据原表达式可知(x+y)≠0，所以取x=（2/3）y代入：x=（2/3）y ，表达式（1）等于 -7/5。

热心网友

解：由3x^2+xy-2y^2=0得(3x-2y)(x+y)=0.由题意可知，x+y≠0，x-y≠0.所以，3x-2y=0.设x=2t,y=3t(t≠0),则[(x+y)/(x-y)+4xy/(y^2-x^2)]/[（x^2+2xy-3y^2)/(x^2-9y^2)]=[(5t)/(-t)+(24t^2)/(9t^2-4t^2)]/[(4t^2+12t^2-27t^2)/(4t^2-81t^2)]=(-5+24/5)/(-11/-77)=-7/5.