Неравенство ln(x+x^2) больше 0

[latex]ln(x+x^2)\ \textgreater \ 0\; ,\\\\ODZ:\; \; x+x^2\ \textgreater \ 0\; ,\; \; x(x+1)\ \textgreater \ 0\; ,\\\\+++(-1)---(0)+++\; \; \; \; \; x\in (-\infty ,-1)\cup (0,+\infty )\\\\ln(x+x^2)\ \textgreater \ ln1\\\\x^2+x\ \textgreater \ 1\\\\x^2+x-1\ \textgreater \ 0\\\\D=1+4=5\; ,\; \; \; x_{1,2}= \frac{-1\pm \sqrt5}{2}\; ;\; \; x_1\approx -1,6\; ,\; x_2\approx 0,6\\\\+++( \frac{-1-\sqrt5}{2} )---( \frac{-1+\sqrt5}{2} )+++ \\\\x\in \Big (-\infty ,\frac{-1-\sqrt5}{2}\Big )\cup \Big ( \frac{-1+\sqrt5}{2}\; ,+\infty \Big )\; \; \; -\; \; otvet[/latex]