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answer:
[tex]\sf -\dfrac{125}{462}[/tex]
step by step explanation:
[tex]\hookrightarrow \sf \dfrac{3}{7} +(-\dfrac{6}{11} ) +(-\dfrac{8}{21} ) +\dfrac{5}{22}[/tex]
\\ rewrite \\
[tex]\hookrightarrow \sf \dfrac{3}{7}-\dfrac{6}{11}-\dfrac{8}{21}+\dfrac{5}{22}[/tex]
\\ least common multiplier of 7, 11, 21, 22 is 462 \\
\\ simplify \\
[tex]\hookrightarrow \sf \dfrac{198}{462}-\dfrac{252}{462}-\dfrac{176}{462}+\dfrac{105}{462}[/tex]
\\ join the fractions together \\
[tex]\hookrightarrow \sf \dfrac{198-252-176+105}{462}[/tex]
\\ simplify - add and subtract\\
[tex]\hookrightarrow \sf \dfrac{-125}{462}[/tex]
\\ simplify by 3 \\
[tex]\sf -\dfrac{125}{462}[/tex]