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

expression for which values of $x$ is positive?
The given expression can also be written as:

$$
\frac{\left(x-\frac{3}{2}\right)^{2}+\frac{3}{4}}{5\left[\left(\frac{7}{10}\right)^{2}-\left(x-\frac{3}{10}\right)^{2}\right]}
$$

The numerator, being the sum of two positive numbers, is positive for all values of \( x \); the fraction is therefore positive if the denominator is positive; that is, if

$\left.1^{\circ}\right)$

$$
\frac{7}{10}>x-\frac{3}{10}, \text { or if } x<\frac{3}{10}+\frac{7}{10}=1, \text { and if } x>\frac{3}{10}-\frac{7}{10}=-\frac{4}{10}=-\frac{2}{5}
$$

The fraction is therefore positive if

$$
-\frac{2}{5}<x<1
$$

(Odön Kornis.)

The problem was also solved by: Breuer M., Freibauer E., Juvancz I., Kárf J., Klein A., Kohn B., Krausz B., Gy. Krisztián, Gy. Lukhaub, M. Mandel, N. Pollák, J. Weisz.