Question

若x2+xy-2y2=0,则(x2+3xy-2y2)/(x2-y2)=?

Answer 1

x^2+xy-2y^2=0分解因式得(x-y)(x+2y)=0,于是x=y或x=-2y

(x^2+3xy-2y^2)/(x^2-y^2)=2xy/[(x+y)(x-y)],此式若有意义,x≠y,于是x=-2y,代入得

(x^2+3xy-2y^2)/(x^2-y^2)=[2*(-2y)*y]/[(-2y+y)*(-2y-y)]=-4/3