Question

已知y/x=1/3，求式子（x^2-y^2）/（x^2+y^2-xy）的值

Answer 1

∵y/x=1/3 ∴x≠0.给原式的分子分母同时除以x²得：原式=[1-（y/x)²]/[1+(y/x)²-(y/x)]=[1-(1/3)²]/[1+(1/3)²-(1/3)]=(8/9)/[(10/9)-(1/3)]=（8/9）/[(10/9)-(3/9)]=(8/9)/(7/9)=8/7。

Answer 2

y/x=1/3
设y=k
x=3k
则
（x^2-y^2）/（x^2+y^2-xy）
=[(3k)^2-k^2)/[(3k)^2+k^2-3k*k]
=8k^2/7k^2
=8/7