Simplify the given mathematical expression:
$\frac{8}{\frac{4}{9}+\frac{16}{9}}$

Answer

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Answer

Finally, simplify the result: $\frac{72}{20}=\boxed{\frac{18}{5}}$

Steps

Step 1 ：First, simplify the denominator: $\frac{4}{9}+\frac{16}{9}=\frac{20}{9}$

Step 2 ：Next, simplify the complex fraction: $\frac{8}{\frac{20}{9}}=8*\frac{9}{20}$

Step 3 ：Then, multiply the numerators and the denominators: $8*\frac{9}{20}=\frac{72}{20}$

Step 4 ：Finally, simplify the result: $\frac{72}{20}=\boxed{\frac{18}{5}}$