Find the value of \(3 \div[(8 – 5) \div \{(4 – 2) + (2 +\frac{8}{13})\}]\)

Given:
$3 \div[(8 - 5) \div {(4 - 2) + (2 + \frac{8}{13})}]$

First simplify inside:

$(8 - 5) = 3$
$(4 - 2) = 2$
Now,
$2 + \frac{8}{13} = \frac{26 + 8}{13} = \frac{34}{13}$

So,
${(4 - 2) + (2 + \frac{8}{13})} = 2 + \frac{34}{13} = \frac{26 + 34}{13} = \frac{60}{13}$

Now expression becomes:

$3 \div \left[ 3 \div \frac{60}{13} \right]$

$3 \div \left[ 3 \times \frac{13}{60} \right]$

$3 \div \frac{39}{60}$

$= 3 \times \frac{60}{39} = \frac{180}{39} = \frac{60}{13}$

Final Answer: $\frac{60}{13}$

Correct option: $\frac{60}{13}$