Question

设f(x-1/x)=(x^3-x)/（x^4+1）,（x不等于0）,求f(x)

Answer 1

分子分母同除以x^2

f(x-1/x)=(x-1/x)/(x^2+1/x^2)

(x-1/x)^2=x^2-2+1/x^2

x^2+1/x^2=(x-1/x)^2+2

所以f(x-1/x)=(x-1/x)/[(x-1/x)^2+2]

所以f(x)=x/(x^2+2)