\(\frac{52}{9}=\frac{45}{9}+\frac{7}{9}=5+\frac{7}{9}=5+\frac{1}{\frac{9}{7}}+5+\frac{1}{\frac{7}{7}+\frac{2}{7}}=5+\frac{1}{1+\frac{1}{\frac{7}{2}}}=5+\frac{1}{1+\frac{1}{\frac{6}{2}+\frac{1}{2}}}\)
\(=5+\frac{1}{1+\frac{1}{3+\frac{1}{2}}}\)
\(\Rightarrow a=1;b=3;c=2\)