Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation

Question

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation

F(x) + F((2x - 3)/x) = x.

Find the function F(x) satisfying these conditions. Write F(x) as a rational function with expanded polynomials in the numerator and denominator.

Answer 1

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation

F(x) = (x^2 - 4x + 3)/(x^2 - 1)