Привет, помогите пожалуйста решить неравенство:

Решение смотрите в приложении.......................

[latex] \frac{4^x-2^{x+4}+30}{2^x-2} + \frac{4^x-7*2^{x}+3}{2^x-7} \leq 2^{x+1}-14[/latex] ОДЗ: [latex] \left \{ {{2^x-2 \neq 0} \atop {2^x-7 \neq 0}} \right. [/latex] [latex]\left \{ {{2^x \neq 2} \atop {2^x \neq 7}} \right. [/latex] [latex]\left \{ {{x \neq 1} \atop {x \neq log_27}} \right. [/latex] [latex]\frac{2^{2x}-16*2^{x}+30}{2^x-2} + \frac{2^{2x}-7*2^{x}+3}{2^x-7} \leq 2*2^{x}-14[/latex] Замена: [latex]2^2=a,[/latex]  [latex]a\ \textgreater \ 0[/latex] [latex]\frac{a^2-16a+30}{a-2} + \frac{a^{2}-7a+3}{a-7} \leq 2a-14[/latex] [latex]\frac{(a-7)(a^2-16a+30)}{(a-2)(a-7)} + \frac{(a-2)(a^{2}-7a+3)}{(a-2)(a-7)} \leq \frac{2(a-7)(a-7)(a-2)}{(a-2)(a-7)} [/latex] [latex]\frac{a^3-7a^2-16a^2+112a+30a-210}{(a-2)(a-7)} + \frac{a^3-7a^2+3a-2a^2+14a-6}{(a-2)(a-7)} \leq \frac{2(a-7)(a-7)(a-2)}{(a-2)(a-7)} [/latex] [latex]\frac{a^3-23a^2+142a-210}{(a-2)(a-7)} + \frac{a^3-9a^2+17a-6}{(a-2)(a-7)} \leq \frac{(a^2-14a+49)(2a-4)}{(a-2)(a-7)} [/latex] [latex]\frac{a^3-23a^2+142a-210+a^3-9a^2+17a-6}{(a-2)(a-7)} \leq \frac{a^3-28a^2+98a-4a^2+56a-196}{(a-2)(a-7)} [/latex] [latex]\frac{2a^3-32a^2+159a-216}{(a-2)(a-7)} \leq \frac{2a^3-32a^2+154a-196}{(a-2)(a-7)} [/latex] [latex]\frac{2a^3-32a^2+159a-216}{(a-2)(a-7)} - \frac{2a^3-32a^2+154a-196}{(a-2)(a-7)} \leq 0[/latex] [latex]\frac{2a^3-32a^2+159a-216-(2a^3-32a^2+154a-196)}{(a-2)(a-7)}\leq 0[/latex] [latex]\frac{2a^3-32a^2+159a-216-2a^3+32a^2-154a+196}{(a-2)(a-7)} \leq 0[/latex] [latex]\frac{5a-20}{(a-2)(a-7)} \leq 0[/latex] [latex]\frac{5(a-4)}{(a-2)(a-7)} \leq 0[/latex] --- - ---(2)----+------[4]---- - -----(7)-----+-------- //////////                   ////////////// ---(0)---------------------------------------------------       ///////////////////////////////////////////////////// [latex]0\ \textless \ a\ \textless \ 2[/latex]           или        [latex]4 \leq a\ \textless \ 7[/latex] [latex]2^x\ \textless \ 2[/latex]                 или       [latex]4 \leq 2^x\ \textless \ 7[/latex] [latex]x\ \textless \ 1[/latex]                   или       [latex]2^2 \leq 2^x\ \textless \ 2^{log_27}[/latex]                                           [latex]2 \leq x\ \textless \ log_27[/latex] Ответ: [latex](-[/latex] ∞ [latex];-1)[/latex] ∪ [latex][2; log_27)[/latex]