#6.57 только а и б, помогите решить. Не могу закончить решение.

Question 1

Question 2

Решите задачу:

$1)\quad \frac{1}{2^{x}-1} +2^{x}\ \textgreater \ 3\; ,\; \; ODZ:\; \; 2^{x}-1\ne 0\; ,\; 2^{x}\ne 1\; ,\; x\ne 0\\\\t=2^{x}\ \textgreater \ 0\; ,\; \; \frac{1}{t-1} +t\ \textgreater \ 3\; ,\; \; \frac{1+t(t-1)-3(t-1)}{t-1} \ \textgreater \ 0\\\\ \frac{1+t^2-t-3t+3}{t-1} \ \textgreater \ 0\; ,\; \; \frac{t^2-4t+4}{t-1} \ \textgreater \ 0\\\\ \frac{(t-2)^2}{t-1} \ \textgreater \ 0\; \; \; ---(1)+++(2)+++\\\\t\in (1,2)\cup (2,+\infty )\\\\a)\; \; 1\ \textless \ t\ \textless \ 2\; ,\; \; 2^0\ \textless \ 2^{x}\ \textless \ 2^1\; \; \to \; \; \; 0\ \textless \ x\ \textless \ 1\\\\b)\; \; t\ \textgreater \ 2\; ,\; \; \; 2^{x}\ \textgreater \ 2\; \; \; \to \; \; \; x\ \textgreater \ 1\\\\x\in (0,1)\cup (1,+\infty )$

$2)\quad \frac{-2}{2^{x}-2} +2^{x}\ \textless \ 3\; ,\; \; ODZ:\; 2^{x}-2\ne 0\; ,\; \; x\ne 1\\\\t=2^{x}\ \textgreater \ 0\; ,\; \; \; \frac{-2}{t-2} +t-3\ \textless \ 0\\\\ \frac{-2+t(t-2)-3(t-2)}{t-2}\ \textless \ 0\; ,\; \; \; \frac{-2+t^2-2t-3t+6}{t-2} \ \textless \ 0\\\\ \frac{t^2-5t+4}{t-2} \ \textless \ 0\; ,\; \; \; \frac{(t-1)(t-4)}{t-2}\ \textless \ 0 \\\\---(1)+++(2)---(4)+++\\\\t\in (-\infty ,1)\cup (2,4)\\\\a)\; \; t\ \textless \ 1\; \; \to \; \; 2^{x}\ \textless \ 1\; ,\; \; \; x\ \textless \ 0\\\\b)\; \; 2\ \textless \ t\ \textless \ 4\; \; \to \; \; \; 2\ \textless \ 2^{x}\ \textless \ 4\; ,\; \; \; 2^1\ \textless \ 2^{x}\ \textless \ 2^2\\\\1\ \textless \ x\ \textless \ 2\\\\Otvet:\; \; \; x\in (-\infty ,0)\cup (1,2)$