ОДЗ: x-1≠ 0 ⇒ x≠ 1
решения:
1*(x-1)} \atop {x \neq 1}} \right. \left \{ {{ax>x-1} \atop {x \neq 1}} \right. \left \{ {{ax-x>-1} \atop {x \neq 1}} \right. \left \{ {{x(a-1)>-1} \atop {x \neq 1}} \right. \left \{ {{x> \frac{-1}{a-1} } \atop {x \neq 1}} \right. \left \{ {{x< \frac{1}{a-1} } \atop {x \neq 1}} \right. " alt=" \left \{ {{ax>1*(x-1)} \atop {x \neq 1}} \right. \left \{ {{ax>x-1} \atop {x \neq 1}} \right. \left \{ {{ax-x>-1} \atop {x \neq 1}} \right. \left \{ {{x(a-1)>-1} \atop {x \neq 1}} \right. \left \{ {{x> \frac{-1}{a-1} } \atop {x \neq 1}} \right. \left \{ {{x< \frac{1}{a-1} } \atop {x \neq 1}} \right. " align="absmiddle" class="latex-formula">