Помогите решить неравенство.

Решите задачу:

$log_5 \frac{3x-2}{x^2+1} \ \textgreater \ 0\; ,\; \; ODZ:\; \frac{3x-2}{x^2+1}\ \textgreater \ 0\; ,\; 3x-2\ \textgreater \ 0\; ,\; x\ \textgreater \ \frac{2}{3}\\\\\log_5 \frac{3x-2}{x^2+1} \ \textgreater \ log_51\\\\\frac{3x-2}{x^2+1} \ \textgreater \ 1\; \; \Rightarrow \; \; \frac{3x-2}{x^2+1} -1\ \textgreater \ 0\; ,\; \; \frac{3x-2-x^2-1}{x^2+1} \ \textgreater \ 0\\\\\\ \frac{-x^2+3x-3}{x^2+1} \ \textgreater \ 0\; ,\; \; \frac{x^2-3x+3}{x^2+1} \ \textless \ 0\; \\\\Tak\; kak\; \; x^2+1\ \textgreater \ 0\; \; pri\; \; x\in R\; ,\; to\; \; x^2-3x+3\ \textless \ 0\; ,\\\\D=9-4\cdot 3=-3\ \textless \ 0\; \; \Rightarrow \; \; \; x^2-3x+3\ \textgreater \ 0\; \; pri\; \; x\in R$

$Otvet:\; x\in (\frac{2}{3},+\infty )\; .$