5. Solve the inequality $\frac{2 x^{2}-6 x+5}{x^{2}-4 x+3}<1$.

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# Solution:

![](https://cdn.mathpix.com/cropped/2024_05_06_8eeeb8d6ace591217257g-16.jpg?height=123&width=575&top_left_y=1843&top_left_x=138)

$$
\frac{2 x^{2}-6 x+5}{x^{2}-4 x+3}<1, \frac{2 x^{2}-6 x+5-x^{2}+4 x-3}{(x-1)(x-3)}<0, \frac{2 x^{2}-2 x+2}{(x-1)(x-3)}<0
$$

Answer: $(1 ; 3)$.