已知x²-3xy-4y²=0(y≠0),求代数式x-y分之x+2y的值

题目

已知x²-3xy-4y²=0(y≠0),求代数式x-y分之x+2y的值

答案

x^2-3xy-4y^2=0
(x-4y)(x+y)=0
x=4y或x=-y
当x=4y时
(x+2y)/(x-y)
=(4y+2y)/(4y-y)
=6y/3y
=2
当x=-y时
(x+2y)/(x-y)
=(-y+2y)/(-y-y)
=y/(-2y)
=-1/2