If (x+2)f(2−x)+(2x+1)f(2+x)=1 for all real values of x, then f(18)=a/b, where a and b are coprime positive integers. What is the value of a+b?

Question

If  (x+2)f(2−x)+(2x+1)f(2+x)=1  for all real values of x, then f(18)=a/b, where a and b are coprime positive integers. What is the value of a+b?

Ms. Sue · Answer

This looks like it's from the independent program, Brilliant. https://brilliant.org/ Maybe you should compete at a lower level.