Question 45
Let $a$, $b$, $c$ be rational numbers such that
$$
\frac{1}{a+bc} + \frac{1}{b+ac} = \frac{1}{a+b}.
$$
Prove that $\sqrt{\frac{c-3}{c+1}}$ is rational.
$$
\frac{1}{a+bc} + \frac{1}{b+ac} = \frac{1}{a+b}.
$$
Prove that $\sqrt{\frac{c-3}{c+1}}$ is rational.