let's firstly convert the mixed fractions to improper fractions, and then add.
[tex]\bf \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}~\hfill \stackrel{mixed}{2\frac{5}{6}}\implies \cfrac{2\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{17}{6}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{13}{4}+\cfrac{17}{6}\implies \stackrel{\textit{we'll use the LCD of 12}}{\cfrac{(3)13~~+~~(2)17}{12}}\implies \cfrac{39+34}{12}\implies \cfrac{73}{12}\implies 6\frac{1}{12}[/tex]
