Đáp án:

\(\begin{array}{l}
13,\\
\dfrac{{28}}{{x + 1}}\\
14,\\
\,\left\{ {x|x \ge  - 15} \right\}\\
15,\\
\left\{ { - 4;1} \right\}\\
16,\\
x = \dfrac{{125}}{{48}}\\
17,\\
x \le \dfrac{{ - 6}}{{17}}
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
13,\\
DKXD:\,\,\,\left\{ \begin{array}{l}
x \ne 1\\
x \ne  - 1
\end{array} \right.\\
H = \left( {\dfrac{{x + 1}}{{x - 1}} - \dfrac{{x - 1}}{{x + 1}}} \right):\dfrac{{3x}}{{7x - 7}}\\
 = \dfrac{{{{\left( {x + 1} \right)}^2} - {{\left( {x - 1} \right)}^2}}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}:\dfrac{{3x}}{{7.\left( {x - 1} \right)}}\\
 = \dfrac{{\left( {{x^2} + 2x + 1} \right) - \left( {{x^2} - 2x + 1} \right)}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}:\dfrac{{3x}}{{7\left( {x - 1} \right)}}\\
 = \dfrac{{{x^2} + 2x + 1 - {x^2} + 2x - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}.\dfrac{{7\left( {x - 1} \right)}}{{3x}}\\
 = \dfrac{{4x}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}.\dfrac{{7\left( {x - 1} \right)}}{{3x}}\\
 = \dfrac{{28}}{{x + 1}}\\
14,\\
8x - 7 \le 9x + 8\\
 \Leftrightarrow \left( {9x + 8} \right) - \left( {8x - 7} \right) \ge 0\\
 \Leftrightarrow 9x + 8 - 8x + 7 \ge 0\\
 \Leftrightarrow x + 15 \ge 0\\
 \Leftrightarrow x \ge  - 15\\
 \Rightarrow Tập\,\,nghiệm\,\,của\,\,bất\,\,phương\,\,trình\,\,là:\,\,\left\{ {x|x \ge  - 15} \right\}\\
15,\\
{x^2} = 4 - 3x\\
 \Leftrightarrow {x^2} - \left( {4 - 3x} \right) = 0\\
 \Leftrightarrow {x^2} - 4 + 3x = 0\\
 \Leftrightarrow \left( {{x^2} + 4x} \right) + \left( { - x - 4} \right) = 0\\
 \Leftrightarrow x\left( {x + 4} \right) - \left( {x + 4} \right) = 0\\
 \Leftrightarrow \left( {x + 4} \right)\left( {x - 1} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
x + 4 = 0\\
x - 1 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x =  - 4\\
x = 1
\end{array} \right.\\
 \Rightarrow Tập\,\,nghiệm\,\,của\,\,phương\,\,trình\,\,là:\,\,\,\,\left\{ { - 4;1} \right\}\\
16,\\
\dfrac{{3x}}{5} + \dfrac{{2x - 1}}{6} = 4 - \dfrac{{2x}}{3}\\
 \Leftrightarrow \dfrac{{6.3x + 5.\left( {2x - 1} \right)}}{{5.6}} = \dfrac{{4.3 - 2x}}{3}\\
 \Leftrightarrow \dfrac{{18x + 10x - 5}}{{30}} = \dfrac{{12 - 2x}}{3}\\
 \Leftrightarrow \dfrac{{28x - 5}}{{30}} = \dfrac{{12 - 2x}}{3}\\
 \Leftrightarrow 3.\left( {28x - 5} \right) = 30.\left( {12 - 2x} \right)\\
 \Leftrightarrow 28x - 5 = 10\left( {12 - 2x} \right)\\
 \Leftrightarrow 28x - 5 = 120 - 20x\\
 \Leftrightarrow 28x + 20x = 120 + 5\\
 \Leftrightarrow 48x = 125\\
 \Leftrightarrow x = \dfrac{{125}}{{48}}\\
17,\\
\dfrac{{3 - 2x}}{{12}} \ge \dfrac{{5x + 3}}{4}\\
 \Leftrightarrow 4.\left( {3 - 2x} \right) \ge 12.\left( {5x + 3} \right)\\
 \Leftrightarrow 3 - 2x \ge 3.\left( {5x + 3} \right)\\
 \Leftrightarrow 3 - 2x \ge 15x + 9\\
 \Leftrightarrow \left( {3 - 2x} \right) - \left( {15x + 9} \right) \ge 0\\
 \Leftrightarrow 3 - 2x - 15x - 9 \ge 0\\
 \Leftrightarrow  - 6 - 17x \ge 0\\
 \Leftrightarrow 6 + 17x \le 0\\
 \Leftrightarrow 17x \le  - 6\\
 \Leftrightarrow x \le \dfrac{{ - 6}}{{17}}
\end{array}\)