Answer:
[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\bf \:(1) \: \: \: - \frac{13}{5} \qquad \: \\ \\& \qquad \:\bf \:(2) \: \: \: \: \: \: \: \frac{12}{11} \end{aligned}} \qquad \\ \\ [/tex]
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-1}}[/tex]
Given expression is
[tex]\sf \:\dfrac{8}{ - 5} + \dfrac{4}{ - 3} + \dfrac{1}{3} \\ \\ [/tex]
[tex]\sf \: = \: - \dfrac{8}{ 5} - \dfrac{4}{3} + \dfrac{1}{3} \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ - 24 - 20 + 5}{ 15} \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ - 44 + 5}{ 15} \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ - 39}{ 15} \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ - 13}{ 5} \\ \\ [/tex]
[tex]\sf \: = \: - \: \dfrac{13}{ 5} \\ \\ [/tex]
Hence,
[tex]\sf\implies \bf \:\dfrac{8}{ - 5} + \dfrac{4}{ - 3} + \dfrac{1}{3} \: = \: - \: \dfrac{13}{5} \\ \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-2}}[/tex]
[tex]\bf \:Subtract \: - \dfrac{9}{11} \: from \: \dfrac{3}{11} \\ \\ [/tex]
That means,
[tex]\sf \:\dfrac{3}{11} - \left( - \dfrac{9}{11} \right) \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{3}{11} + \dfrac{9}{11} \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{3 + 9}{11} \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{12}{11} \\ \\ [/tex]
Hence,
[tex]\sf\implies \bf \:\dfrac{3}{11} - \left( - \dfrac{9}{11} \right) \: = \: \dfrac{12}{11} \\ \\ [/tex]