Question 10
Let $\mathbb{R}^{\star}$ be the set of all real numbers, except $1$. Find all functions $f: \mathbb{R}^{\star} \rightarrow \mathbb{R}$ that satisfy the functional equation
$$
x + f(x) + 2 f\left(\frac{x+2009}{x-1}\right) = 2010
$$
$$
x + f(x) + 2 f\left(\frac{x+2009}{x-1}\right) = 2010
$$