Question 31
Find all real numbers $x$ such that $-1 \lt x \leq 2$ and
$$
\sqrt{2 - x} + \sqrt{2 + 2x} = \sqrt{\frac{x^{4} + 1}{x^{2} + 1}} + \frac{x + 3}{x + 1}.
$$
$$
\sqrt{2 - x} + \sqrt{2 + 2x} = \sqrt{\frac{x^{4} + 1}{x^{2} + 1}} + \frac{x + 3}{x + 1}.
$$