We have the expression:
[tex]4\frac{2}{3}+2\frac{3}{x}=7\frac{5}{12}[/tex]and we have to find the missing number (x):
[tex]\begin{gathered} 4\frac{2}{3}+2\frac{3}{x}=7\frac{5}{12} \\ 4+2+\frac{2}{3}+\frac{3}{x}=7+\frac{5}{12} \\ 6+\frac{2}{3}+\frac{3}{x}=7+\frac{5}{12} \\ \frac{3}{x}=7+\frac{5}{12}-6-\frac{2}{3} \\ \frac{3}{x}=1+\frac{5}{12}-\frac{2}{3} \\ \frac{3}{x}=1+\frac{5-2\cdot4}{12} \\ \frac{3}{x}=1+\frac{5-8}{12} \\ \frac{3}{x}=1-\frac{3}{12} \\ \frac{3}{x}=\frac{12-3}{12} \\ \frac{3}{x}=\frac{9}{12} \\ 3\cdot12=9\cdot x \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \end{gathered}[/tex]Answer: the missing number is 4.
