若x/y=-2,x^2-2xy-3y^2/x^2-6xy-7y^2的值

本题解答的要点是要对原式进行因式分解.如下：
原式=[x^2-2xy+y^2-4y^2]/[x^2-6xy+9y^2-16y^2]
=[(x-y)^2-4y^2]/[(x-3y)^2-16y^2]
=[(x-y+2y)(x-y-2y)]/[(x-3y+4y)(x-3y-4y)]
=[(x+y)(x-3y)]/[(x+y)(x-7y)]
=(x-3y)/(x-7y)
把x/y=-2带入上式
得：=(-2y-3y)/(-2y-7y)
=5/9