$\sqrt{log_a(\frac{3-2x}{1-x})}<1$ wolfram's solution: $1 < a < 2, 2 \leq x < \frac{a-3}{a-2}\\ a=2, x \geq 2\\ a >2, x < \frac{a-3}{a-2}\\ a > 2, x \geq 2\\ 0 < a < 1, \frac{a-3}{a-2}< x \leq2 $\
I try
$ D:\boxed{ \frac{3-2x}{1-x} > 0 \rightarrow x < 1 ~or ~x > \frac{3}{2}\\ and~log_a\frac{3-2x}{1-x}\geq0\rightarrow x\leq 1~or~x \geq \frac{3}{2},~if~a > 1\\ and ~log_a\frac{3-2x}{1-x} \leq 0 \rightarrow1 \leq x \leq\frac{3}{2}, if~ 0 < a < 1\\ and ~x\neq 1}\\ If~a > 1\rightarrow log_a\frac{3-2x}{1-x}< 1 \rightarrow x <\frac{a-3}{a-2}\\ If ~0 < a < 1 \rightarrow log_a \frac{3-2x}{1-x} > 1 \rightarrow x > \frac{a-3}{a-2}$
But I couldn't put the solutions together. Can someone help?