The value of $$\frac{5}{5+\frac{1}{4-\frac{1}{\frac78}}}+\frac{7}{107}$$​ is:

Correct option is C

Given:
Expression: $$\frac{5}{5+\frac{1}{4-\frac{1}{\frac78}}}+\frac{7}{107}$$​​
Solution:
​$$\frac{5}{5+\frac{1}{4-\frac{1}{7/8}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{1}{4-\frac{8}{7}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{1}{\frac{28}{7}-\frac{8}{7}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{1}{\frac{20}{7}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{7}{20}}+\frac{7}{107} \\ \ \\= \frac{5}{\frac{100}{20}+\frac{7}{20}}+\frac{7}{107} \\ \ \\= \frac{5}{\frac{107}{20}}+\frac{7}{107} \\ \ \\= \frac{5 \times 20}{107}+\frac{7}{107} \\ \ \\= \frac{100}{107}+\frac{7}{107} \\ \ \\= \frac{107}{107} \\ \ \\= 1$$​​