Simplify :

$3 \div \Big[3\times \left\lbrace3 - \Big(3 - \dfrac{1}{4}\Big)\right\rbrace \Big]$

$\Rightarrow 3 \div \Big[3\times \left\lbrace3 - \Big(3 - \dfrac{1}{4}\Big)\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace3 - \Big(\dfrac{3}{1} - \dfrac{1}{4}\Big)\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace3 - \Big(\dfrac{3 \times 4}{1 \times 4} - \dfrac{1}{4}\Big)\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace3 - \Big(\dfrac{12}{4} - \dfrac{1}{4}\Big)\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace3 - \Big(\dfrac{12 - 1}{4}\Big)\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace3 - \Big(\dfrac{11}{4}\Big)\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace\dfrac{3}{1} - \dfrac{11}{4}\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace\dfrac{3 \times 4}{1 \times 4} - \dfrac{11}{4}\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace\dfrac{12}{4} - \dfrac{11}{4}\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace\dfrac{12 - 11}{4}\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[3\times \left\lbrace\dfrac{1}{4}\right\rbrace \Big]\\[1em] \Rightarrow 3 \div \Big[\dfrac{3 \times 1}{4} \Big]\\[1em] \Rightarrow 3 \div \dfrac{3}{4}\\[1em] \Rightarrow 3 \times \dfrac{4}{3}\\[1em] \Rightarrow \dfrac{4 \times 3}{3}\\[1em] \Rightarrow 4$

Hence, $3 \div \Big[3\times \left\lbrace3 - \Big(3 - \dfrac{1}{4}\Big)\right\rbrace \Big] = 4$.