Question 21
Consider the function
$$
f(x) = \frac{(x-2)(x+1)(2x-1)}{x(x-1)}
$$
Suppose that $u$ and $v$ are real numbers such that
$$
f(u) = f(v).
$$
Suppose that $u$ is rational. Prove that $v$ is rational.
$$
f(x) = \frac{(x-2)(x+1)(2x-1)}{x(x-1)}
$$
Suppose that $u$ and $v$ are real numbers such that
$$
f(u) = f(v).
$$
Suppose that $u$ is rational. Prove that $v$ is rational.