first off, we'd convert the mixed fractions to "improper", then get the LCD to sum them up.
[tex]\bf \stackrel{mixed}{2\frac{3}{8}}\implies \cfrac{2\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{19}{8}}
\\\\\\
\stackrel{mixed}{3\frac{3}{7}}\implies \cfrac{3\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{24}{7}}\\\\
-------------------------------\\\\
\cfrac{19}{8}+\cfrac{24}{7}\impliedby \textit{so our LCD is just 56}\implies \cfrac{(7\cdot 19)~+~(8\cdot 24)}{56}
\\\\\\
\cfrac{133+192}{56}\implies \cfrac{325}{56}\implies 5\frac{45}{56}[/tex]
