\(x\)
\({-}13\)
\({-5}\)
\({-}0{,}2\)
\(0\)
\(\frac{1}{17}\)
\(1\)
\(5\frac{2}{3}\)
\(7\)
\(\frac{x+5}{x-3}\)
\(\frac{1}{2}\)
\(0\)
\({-}1\frac{1}{2}\)
\({-}1\frac{2}{3}\)
\({-}1\frac{18}{25}\)
\({-}3\)
\(4\)
\(3\)
\(\begin{array}[t]{ll}{\largeПри}\ x={-}13\phantom{,}&&\frac{x+5}{x-3}=\frac{{-}13+5}{{-}13-3}=\frac{{-}8}{{-}16}=\frac{1}{2}=0{,}5;\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x={-}5\phantom{,0}&&\frac{x+5}{x-3}=\frac{{-}5+5}{{-}5-3}=\frac{0}{{-}8}=0;\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x={-}0{,}2&&\frac{x+5}{x-3}=\frac{{-}0{,}2+5}{{-}0{,}2-3}=\frac{4{,}8}{{-}3{,}2}={-}\frac{48}{32}={-}\frac{3}{2}={-}1\frac{1}{2}={-}1{,}5;\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x=0\phantom{-,0}&&\frac{x+5}{x-3}=\frac{0+5}{0-3}=\frac{5}{{-}3}={-}1\frac{2}{3};\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x=\frac{1}{17}\phantom{-}&&\frac{x+5}{x-3}=\frac{\frac{1}{17}+5}{\frac{1}{17}-3}=\frac{\frac{1}{17}+\frac{85}{17}}{\frac{1}{17}-\frac{51}{17}}=\frac{86}{17}:\left({-}\frac{50}{17}\right)=\frac{86}{17}\cdot\left({-}\frac{17}{50}\right)={-}\frac{43}{25}={-}1\frac{18}{25};\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x=1\phantom{-,0}&&\frac{x+5}{x-3}=\frac{1+5}{1-3}=\frac{6}{{-}2}={-}3;\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x=5\frac{2}{3}\phantom{-}&&\frac{x+5}{x-3}=\frac{5\frac{2}{3}+5}{5\frac{2}{3}-3}=10\frac{2}{3}:2\frac{2}{3}=\frac{32}{3}:\frac{8}{3}=\frac{32}{3}\cdot\frac{3}{8}=4;\end{array}\)
\(\begin{array}[t]{ll}{\largeПри}\ x=7\phantom{-,0}&&\frac{x+5}{x-3}=\frac{7+5}{7-3}=\frac{12}{4}=3.\end{array}\)