已知y/x-x/y=-5,求分式3x^2+xy-3y^2/2x^2-xy-2y^2的值

Question

已知y/x-x/y=-5,求分式3x^2+xy-3y^2/2x^2-xy-2y^2的值

Answer 1

y/x-x/y=-5,
两边乘xy得
y^2-x^2=-5xy
(3x^2+xy-3y^2)/(2x^2-xy-2y^2)
=(15xy+xy)/(10xy-xy)
=16/9