设f(x+y,y/x)=x^2-y^2(y-1),则f(x,y)等于什么?希望能有详细步骤,谢谢了.

Question

设f(x+y,y/x)=x^2-y^2(y-1),则f(x,y)等于什么 ? 希望能有详细步骤,谢谢了.

Answer 1

x^2-y^2=(x/y-y/x)xy=(x/y-y/x)(x+y)^2/(x/y+y/x+2) 则f(x,y)=(1/y-y)x^2/(y+1/y+2)