Let's simplify the following fractions:

$$
\begin{array}{ll}
\text { 1. } \frac{a \sqrt{x}-x \sqrt{a}}{\sqrt{a}-\sqrt{x}} & \text { 2. } \frac{\sqrt{a+b}-\sqrt{a-b}}{a+b-\sqrt{a^{2}-b^{2}}}
\end{array}
$$
$$
\begin{gathered}
\text { 1. } \frac{a \sqrt{x}-x \sqrt{a}}{\sqrt{a}-\sqrt{x}}=\frac{\sqrt{a x}(\sqrt{a}-\sqrt{x})}{\sqrt{a}-\sqrt{x}}=\sqrt{a x} \\
\text { 2. } \left.\frac{\sqrt{a+b}-\sqrt{a-b}}{a+b-\sqrt{a^{2}-b^{2}}}=\frac{\sqrt{a+b}-\sqrt{a-b}}{\sqrt{a+b}(\sqrt{a+b}-\sqrt{a-b})}\right)=\frac{1}{\sqrt{a+b}}=\frac{\sqrt{a+b}}{a+b}
\end{gathered}
$$

(Klein Gyula, ág.h.ev.fg. Budapest.)

Number of solutions: 32.

Translation:
$$
\begin{gathered}
\text { 1. } \frac{a \sqrt{x}-x \sqrt{a}}{\sqrt{a}-\sqrt{x}}=\frac{\sqrt{a x}(\sqrt{a}-\sqrt{x})}{\sqrt{a}-\sqrt{x}}=\sqrt{a x} \\
\text { 2. } \left.\frac{\sqrt{a+b}-\sqrt{a-b}}{a+b-\sqrt{a^{2}-b^{2}}}=\frac{\sqrt{a+b}-\sqrt{a-b}}{\sqrt{a+b}(\sqrt{a+b}-\sqrt{a-b})}\right)=\frac{1}{\sqrt{a+b}}=\frac{\sqrt{a+b}}{a+b}
\end{gathered}
$$

(Klein Gyula, ág.h.ev.fg. Budapest.)

Number of solutions: 32.
$$