Simplify: \(\dfrac{\left(\frac{16}{21}\right)}{\left(\frac{16}{4}\right)} \div \left(\dfrac{4}{5}\times\dfrac{10}{12}+\dfrac{4}{7}\right)+\dfrac{4}{8}\div\dfrac{26}{14}\text{ of }\dfrac{14}{8}\)
\(\tfrac{4}{13}\)
\(\dfrac{16/21}{16/4} = \dfrac{16}{21}\times\dfrac{4}{16} = \dfrac{4}{21}\).
Inside the bracket: \(\dfrac45\times\dfrac{10}{12}=\dfrac23\), plus \(\dfrac47\) gives \(\dfrac23+\dfrac47=\dfrac{26}{21}\).
First part: \(\dfrac{4}{21}\div\dfrac{26}{21} = \dfrac{4}{26} = \dfrac{2}{13}\).
For the second part, \(\dfrac48=\dfrac12\), and \(\dfrac{26}{14}\text{ of }\dfrac{14}{8} = \dfrac{26}{8}=\dfrac{13}{4}\), so \(\dfrac12\div\dfrac{13}{4} = \dfrac12\times\dfrac{4}{13}=\dfrac{2}{13}\).
Adding both parts: \(\dfrac{2}{13}+\dfrac{2}{13} = \dfrac{4}{13}\).
Hence, the simplified value of the expression is \(\tfrac{4}{13}\).
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