Решение:

Нам нужно вычислить значение выражения $$\frac{x+5}{x-3}$$ для каждого значения x, указанного в таблице.

1. x = -13:

   $$ \frac{-13 + 5}{-13 - 3} = \frac{-8}{-16} = \frac{1}{2} = 0.5 $$

2. x = -5:

   $$ \frac{-5 + 5}{-5 - 3} = \frac{0}{-8} = 0 $$

3. x = -0.2:

   $$ \frac{-0.2 + 5}{-0.2 - 3} = \frac{4.8}{-3.2} = -1.5 $$

4. x = 0:

   $$ \frac{0 + 5}{0 - 3} = \frac{5}{-3} = -\frac{5}{3} = -1\frac{2}{3} \approx -1.6667 $$

5. x = $$\frac{1}{17}$$:

   $$ \frac{\frac{1}{17} + 5}{\frac{1}{17} - 3} = \frac{\frac{1 + 85}{17}}{\frac{1 - 51}{17}} = \frac{\frac{86}{17}}{\frac{-50}{17}} = \frac{86}{-50} = -\frac{43}{25} = -1.72 $$

6. x = 1:

   $$ \frac{1 + 5}{1 - 3} = \frac{6}{-2} = -3 $$

7. x = $$5\frac{2}{3} = \frac{17}{3}$$:

   $$ \frac{\frac{17}{3} + 5}{\frac{17}{3} - 3} = \frac{\frac{17 + 15}{3}}{\frac{17 - 9}{3}} = \frac{\frac{32}{3}}{\frac{8}{3}} = \frac{32}{8} = 4 $$

8. x = 7:

   $$ \frac{7 + 5}{7 - 3} = \frac{12}{4} = 3 $$

Заполненная таблица: