Giải thích các bước giải:
ĐKXĐ: x$ \ne $0
$\begin{gathered} {\frac{1}{3}^{\frac{2}{x}}} + 3.{\frac{1}{3}^{\frac{1}{x} + 1}} > 12 \hfill \\ \Leftrightarrow {({\frac{1}{3}^{\frac{1}{x}}})^2} + 3.\frac{1}{3}.{\frac{1}{3}^{\frac{1}{x}}} > 12 \hfill \\ \Leftrightarrow {({\frac{1}{3}^{\frac{1}{x}}})^2} + {\frac{1}{3}^{\frac{1}{x}}} - 12 > 0 \hfill \\ \Leftrightarrow ({\frac{1}{3}^{\frac{1}{x}}} + 4)({\frac{1}{3}^{\frac{1}{x}}} - 3) > 0 \hfill \\ \Leftrightarrow \left[ \begin{gathered} {\frac{1}{3}^{\frac{1}{x}}} + 4 > 0 \hfill \\ {\frac{1}{3}^{\frac{1}{x}}} - 3 < 0 \hfill \\ \end{gathered} \right.(do\,{\frac{1}{3}^{\frac{1}{x}}} + 4 > {\frac{1}{3}^{\frac{1}{x}}} - 3\forall tm\,DKXD) \hfill \\ \Leftrightarrow \left[ \begin{gathered} {\frac{1}{3}^{\frac{1}{x}}} - 3 > 0 \hfill \\ {\frac{1}{3}^{\frac{1}{x}}} + 4 < 0(vo\,li\,do{\frac{1}{3}^{\frac{1}{x}}} > 0\forall x\,tm\,DKXD)\, \hfill \\ \end{gathered} \right. \hfill \\ \Leftrightarrow {\frac{1}{3}^{\frac{1}{x}}} > 3 \hfill \\ \Leftrightarrow {\frac{1}{3}^{\frac{1}{x}}} > {\frac{1}{3}^{ - 1}} \hfill \\ \Leftrightarrow \frac{1}{x} < - 1(do\,\frac{1}{3} < 1) \hfill \\ \Leftrightarrow \frac{1}{x} + 1 < 0 \hfill \\ \Leftrightarrow \frac{{1 + x}}{x} < 0 \hfill \\ \Leftrightarrow \left\{ \begin{gathered} 1 + x > 0 \hfill \\ x < 0 \hfill \\ \end{gathered} \right.(do\,1 + x > x) \hfill \\ \Leftrightarrow \left\{ \begin{gathered} x > - 1 \hfill \\ x < 0 \hfill \\ \end{gathered} \right. \hfill \\ \Leftrightarrow - 1 < x < 0 \hfill \\ \end{gathered} $
