![x-2< \frac{12}{x-1} // (x-2)(x-1)<12 // x=[-;]U[10];[13]](https://tex.z-dn.net/?f=+x-2%3C+%5Cfrac%7B12%7D%7Bx-1%7D+%2F%2F+%28x-2%29%28x-1%29%3C12+%2F%2F+x%3D%5B-%3B%5DU%5B10%5D%3B%5B13%5D+ "x-2< \frac{12}{x-1} // (x-2)(x-1)<12 // x=[-;]U[10];[13]")
log_{\frac{1}{9}}(x+15) \\
log_{\frac{1}{3}}(x+3)>log_{\frac{1}{3}}^_{2}(x+15) \\
log_{\frac{1}{3}(x+3)>\frac{1}{2}log_{\frac{1}{3}(x+15) \\ " alt=" log_{\frac{1}{3}}(x+3)>log_{\frac{1}{9}}(x+15) \\
log_{\frac{1}{3}}(x+3)>log_{\frac{1}{3}}^_{2}(x+15) \\
log_{\frac{1}{3}(x+3)>\frac{1}{2}log_{\frac{1}{3}(x+15) \\ " align="absmiddle" class="latex-formula">
\sqrt{x+15} \\
x^{2}+6x+9>x+15 \\
x^{2}-5x-6>0 \\ " alt=" x+3>\sqrt{x+15} \\
x^{2}+6x+9>x+15 \\
x^{2}-5x-6>0 \\ " align="absmiddle" class="latex-formula">
x_{1}=6 \ x_{2}=-1 " alt=" x_{1,2}=\frac{5+-\sqrt{25+24}}{2} \\
x_{1}=6 \ x_{2}=-1 " align="absmiddle" class="latex-formula">