Question 1209953
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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 \left( \frac{2x - 3}{x - 1} \right) + F \left( \frac{1}{x} \right) = x.
Find the function F(x) satisfying these conditions.  
Write F(x) as a rational function with expanded polynomials in the numerator and denominator.
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In his post,  @CPhill gives the answer to the problem    F(x) = {{{(2x^3 - 4x^2 + 2x + 1)/(5x^2 - 5x)}}}.



This answer is incorrect, since this function from the @CPhill's post is defined for all real x except of x= 0 and x= 1,


while the problem requires the function  F(x)  to be defined for all real x except for x = 1 and x = 2.