Let's simplify the following fractions:

$$
\frac{2 x^{3}+x^{2}-8 x+5}{7 x^{2}-12 x+5}, \quad \frac{2 x^{3}+3 x^{2}+x}{x^{3}-x^{2}-2 x}
$$
The greatest common divisor of the numerator and denominator in the first case is $x-1$, and in the second case, it is $x^{2}+x$. After simplifying the fractions with these expressions, we get:

$$
\frac{2 x^{2}+3 x-5}{7 x-5}, \frac{2 x+1}{x-2}
$$

(Dsida Jenö, Gyór.)

Number of solutions: 31.