The reciprocal of the value of  $$ 3 \frac{1}{2} - [ 1 - \frac{3}{4} +$$ { 2$$\frac{1}{2} - (1\frac{1}{2} - \frac{1}{3})$$ } ] 

= $$ 3 \frac{1}{2} - [ 1 - \frac{3}{4} +$$ { 2$$\frac{1}{2} - (1\frac{1}{2} - \frac{1}{3})$$ } ] 

= $$ 3 \frac{1}{2} - [ 1 - \frac{3}{4} +$$ { $$\frac{5}{2} - (\frac{3}{2} - \frac{1}{3})$$ } ] 

= $$  \frac{7}{2} - [ 1 - \frac{3}{4} +$$ $$\frac{8}{6}$$ ] 

= $$  \frac{7}{2} - [ 1 - \frac{3}{4} +$$ $$\frac{8}{6}$$ ] 

= $$  \frac{7}{2} - [ 1 - \frac{25}{12}$$ ] 

= $$  \frac{7}{2} - [ - \frac{13}{12}$$ ] 

= $$  \frac{7}{2} - [ - \frac{13}{12}$$ ]