0\\\\20t^2-21\cdot t\cdot \frac{1}{2}+1\leq 0\ \ \ \to \ \ \ 40t^2-21t+2\leq 0\ \ ,\ \ D=121\ ," alt="\left\{\begin{array}{l}5\cdot 2^{2x+2}-21\cdot 2^{x}-1+1\leq 0\\\dfrac{x^2+2x+2}{x^2+2x}+\dfrac{3x+1}{x-1}\leq \dfrac{4x+1}{x}\end{array}\right\\\\\\1)\ \ 5\cdot 2^{2x+2}-21\cdot 2^{x}-1+1\leq 0\ \ ,\\\\5\cdot 2^{2x}\cdot 2^2-21\cdot 2^{x}\cdot \frac{1}{2}+1\leq 0\ \ ,\ \ \ t=2^{x}>0\\\\20t^2-21\cdot t\cdot \frac{1}{2}+1\leq 0\ \ \ \to \ \ \ 40t^2-21t+2\leq 0\ \ ,\ \ D=121\ ," align="absmiddle" class="latex-formula">
![t_1=\frac{1}{8}\ \ ,\ \ t_2=\frac{2}{5}\ \ ,\ \ 40(t-\frac{1}{8})(t-\frac{2}{5})\leq 0\ \ \ \to \ \ t\in [\ \frac{1}{8}\, ;\, \frac{2}{5}\; ]](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7B1%7D%7B8%7D%5C%20%5C%20%2C%5C%20%5C%20t_2%3D%5Cfrac%7B2%7D%7B5%7D%5C%20%5C%20%2C%5C%20%5C%2040%28t-%5Cfrac%7B1%7D%7B8%7D%29%28t-%5Cfrac%7B2%7D%7B5%7D%29%5Cleq%200%5C%20%5C%20%5C%20%5Cto%20%5C%20%5C%20t%5Cin%20%5B%5C%20%5Cfrac%7B1%7D%7B8%7D%5C%2C%20%3B%5C%2C%20%5Cfrac%7B2%7D%7B5%7D%5C%3B%20%5D "t_1=\frac{1}{8}\ \ ,\ \ t_2=\frac{2}{5}\ \ ,\ \ 40(t-\frac{1}{8})(t-\frac{2}{5})\leq 0\ \ \ \to \ \ t\in [\ \frac{1}{8}\, ;\, \frac{2}{5}\; ]")
![2)\ \ \dfrac{(x^2+2x)+2}{x^2+2x}+\dfrac{3x+1}{x-1}\leq \dfrac{4x+1}{x}\\\\1+\dfrac{2}{x(x+2)}+3+\dfrac{4}{x-1}\leq 4+\dfrac{1}{x}\\\\\dfrac{2}{x(x+2)}+\dfrac{4}{x-1}-\dfrac{1}{x} \leq 0\\\\\\\dfrac{2(x-1)+4x(x+2)-(x+2)(x-1)}{x(x+2)(x-1)}\leq 0\\\\\\\dfrac{3x^2+9x}{x(x+2)(x-1)}\leq 0\ \ ,\ \ \ \dfrac{3\, (x+3)}{(x+2)(x-1)}\leq 0\\\\\\znaki:\ \ \ ---[-3\, ]+++(-2)---(1)+++\\\\x\in (-\infty ;-3\; ]\cup (-2;\, 1\, )](https://tex.z-dn.net/?f=2%29%5C%20%5C%20%5Cdfrac%7B%28x%5E2%2B2x%29%2B2%7D%7Bx%5E2%2B2x%7D%2B%5Cdfrac%7B3x%2B1%7D%7Bx-1%7D%5Cleq%20%5Cdfrac%7B4x%2B1%7D%7Bx%7D%5C%5C%5C%5C1%2B%5Cdfrac%7B2%7D%7Bx%28x%2B2%29%7D%2B3%2B%5Cdfrac%7B4%7D%7Bx-1%7D%5Cleq%204%2B%5Cdfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5Cdfrac%7B2%7D%7Bx%28x%2B2%29%7D%2B%5Cdfrac%7B4%7D%7Bx-1%7D-%5Cdfrac%7B1%7D%7Bx%7D%20%5Cleq%200%5C%5C%5C%5C%5C%5C%5Cdfrac%7B2%28x-1%29%2B4x%28x%2B2%29-%28x%2B2%29%28x-1%29%7D%7Bx%28x%2B2%29%28x-1%29%7D%5Cleq%200%5C%5C%5C%5C%5C%5C%5Cdfrac%7B3x%5E2%2B9x%7D%7Bx%28x%2B2%29%28x-1%29%7D%5Cleq%200%5C%20%5C%20%2C%5C%20%5C%20%5C%20%5Cdfrac%7B3%5C%2C%20%28x%2B3%29%7D%7B%28x%2B2%29%28x-1%29%7D%5Cleq%200%5C%5C%5C%5C%5C%5Cznaki%3A%5C%20%5C%20%5C%20---%5B-3%5C%2C%20%5D%2B%2B%2B%28-2%29---%281%29%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%28-%5Cinfty%20%3B-3%5C%3B%20%5D%5Ccup%20%28-2%3B%5C%2C%201%5C%2C%20%29 "2)\ \ \dfrac{(x^2+2x)+2}{x^2+2x}+\dfrac{3x+1}{x-1}\leq \dfrac{4x+1}{x}\\\\1+\dfrac{2}{x(x+2)}+3+\dfrac{4}{x-1}\leq 4+\dfrac{1}{x}\\\\\dfrac{2}{x(x+2)}+\dfrac{4}{x-1}-\dfrac{1}{x} \leq 0\\\\\\\dfrac{2(x-1)+4x(x+2)-(x+2)(x-1)}{x(x+2)(x-1)}\leq 0\\\\\\\dfrac{3x^2+9x}{x(x+2)(x-1)}\leq 0\ \ ,\ \ \ \dfrac{3\, (x+3)}{(x+2)(x-1)}\leq 0\\\\\\znaki:\ \ \ ---[-3\, ]+++(-2)---(1)+++\\\\x\in (-\infty ;-3\; ]\cup (-2;\, 1\, )")
![3)\ \ \left\{\begin{array}{l}t\in [\; \frac{1}{8}\, ;\, \frac{2}{5}\; ]\\x\in (-\infty ;-3\; ]\cup (-2\, ;\, 1\, )\end{array}\right\ \ \left\{\begin{array}{l}2^{-3}\leq 2^{x}\leq 2^{log_2(2/5)}\\x\in (-\infty ;-3\; ]\cup (-2\, ;\, 1\, )\end{array}\right\\\\\\\left\{\begin{array}{l}x\in [\, -3\, ;\, log_2\frac{2}{5}\; ]\\\x\in (-\infty ;-3\; ]\cup (-2\, ;\, 1\, )\end{array}\right\ \ \Rightarrow \ \ \ x\in \{-3\}\cup (\; -2;log_2\frac{2}{5}\, )](https://tex.z-dn.net/?f=3%29%5C%20%5C%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dt%5Cin%20%5B%5C%3B%20%5Cfrac%7B1%7D%7B8%7D%5C%2C%20%3B%5C%2C%20%5Cfrac%7B2%7D%7B5%7D%5C%3B%20%5D%5C%5Cx%5Cin%20%28-%5Cinfty%20%3B-3%5C%3B%20%5D%5Ccup%20%28-2%5C%2C%20%3B%5C%2C%201%5C%2C%20%29%5Cend%7Barray%7D%5Cright%5C%20%5C%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D2%5E%7B-3%7D%5Cleq%202%5E%7Bx%7D%5Cleq%202%5E%7Blog_2%282%2F5%29%7D%5C%5Cx%5Cin%20%28-%5Cinfty%20%3B-3%5C%3B%20%5D%5Ccup%20%28-2%5C%2C%20%3B%5C%2C%201%5C%2C%20%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%5Cin%20%5B%5C%2C%20-3%5C%2C%20%3B%5C%2C%20log_2%5Cfrac%7B2%7D%7B5%7D%5C%3B%20%5D%5C%5C%5Cx%5Cin%20%28-%5Cinfty%20%3B-3%5C%3B%20%5D%5Ccup%20%28-2%5C%2C%20%3B%5C%2C%201%5C%2C%20%29%5Cend%7Barray%7D%5Cright%5C%20%5C%20%5CRightarrow%20%5C%20%5C%20%5C%20x%5Cin%20%5C%7B-3%5C%7D%5Ccup%20%28%5C%3B%20-2%3Blog_2%5Cfrac%7B2%7D%7B5%7D%5C%2C%20%29 "3)\ \ \left\{\begin{array}{l}t\in [\; \frac{1}{8}\, ;\, \frac{2}{5}\; ]\\x\in (-\infty ;-3\; ]\cup (-2\, ;\, 1\, )\end{array}\right\ \ \left\{\begin{array}{l}2^{-3}\leq 2^{x}\leq 2^{log_2(2/5)}\\x\in (-\infty ;-3\; ]\cup (-2\, ;\, 1\, )\end{array}\right\\\\\\\left\{\begin{array}{l}x\in [\, -3\, ;\, log_2\frac{2}{5}\; ]\\\x\in (-\infty ;-3\; ]\cup (-2\, ;\, 1\, )\end{array}\right\ \ \Rightarrow \ \ \ x\in \{-3\}\cup (\; -2;log_2\frac{2}{5}\, )")