1A. Solve the irrational equation

$$
\frac{\sqrt{x^{2}+x+6}+\sqrt{x^{2}-x-4}}{\sqrt{x^{2}+x+6}-\sqrt{x^{2}-x-4}}=5
$$
Solution. For $x \neq-5$ we have:

$$
\begin{aligned}
\frac{\sqrt{x^{2}+x+6}+\sqrt{x^{2}-x-4}}{\sqrt{x^{2}+x+6}-\sqrt{x^{2}-x-4}}=5 & \Leftrightarrow \sqrt{x^{2}+x+6}+\sqrt{x^{2}-x-4}=5 \sqrt{x^{2}+x+6}-5 \sqrt{x^{2}-x-4} \\
& \Leftrightarrow 6 \sqrt{x^{2}-x-4}=4 \sqrt{x^{2}+x+6} \\
& \Leftrightarrow 3 \sqrt{x^{2}-x-4}=2 \sqrt{x^{2}+x+6} .
\end{aligned}
$$

Squaring the last equation, we get

$$
9\left(x^{2}-x-4\right)=4\left(x^{2}+x+6\right) \quad \Leftrightarrow \quad 5 x^{2}-13 x-60=0 \quad \Leftrightarrow \quad x_{1}=5, x_{2}=-\frac{12}{5}
$$

By checking, it is confirmed that both solutions belong to the domain and are solutions to the original equation.