\[\boxed{\text{290}\text{\ (290)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{2^{\backslash x + 3}}{x - 2} - \frac{10^{\backslash x - 2}}{x + 3} =\]
\[= \frac{50}{x^{2} + x - 6} - 1^{\backslash x^{2} + x - 6}\]
\[x^{2} + x - 6 = (x + 3)(x - 2)\]
\[x_{1} + x_{2} = - 1;\ \ \ x_{1} \cdot x_{2} = - 6\]
\[x_{1} = - 3;\ \ x_{2} = 2.\]
\[\frac{x^{2} - 7x - 30}{(x - 2)(x + 3)} = 0\]
\[x^{2} - 7x - 30 = (x + 3)(x - 10)\]
\[x_{1} + x_{2} = 7;\ \ \ x_{1} \cdot x_{2} = - 30\]
\[x_{1} = 10;\ \ \ \ x_{2} = - 3.\]
\[\frac{(x - 10)(x + 3)}{(x - 2)(x + 3)} = 0\]
\[\frac{x - 10}{x - 2} = 0\]
\[x - 10 = 0\]
\[x = 10.\]
\[Ответ:x = 10.\]
\[\textbf{б)}\ \frac{x + 5^{\backslash x - 7}}{x - 1} + \frac{2x - 5^{\backslash x - 1}}{x - 7} -\]
\[- \frac{30 - 12x}{8x - x^{2} - 7} = 0\]
\[x^{2} - 8x + 7 = (x - 1)(x - 7)\]
\[D_{1} = 16 - 9 = 9\]
\[x_{1} = 4 + 3 = 7;\ \ x_{2} = 4 - 3 = 1.\]
\[= 0;\ \ \ \ x \neq 1;\ \ x \neq 7\]
\[\frac{3x^{2} - 21x}{(x - 1)(x - 7)} = 0\]
\[\frac{3x(x - 7)}{(x - 1)(x - 7)} = 0\]
\[\frac{3x}{x - 1} = 0\]
\[3x = 0\]
\[x = 0.\]
\[Ответ:x = 0.\]