Solve Complex Fraction Expression: (10/7)/2 + 2/(7/8)

To solve the expression $\frac{\frac{10}{7}}{2}+\frac{2}{\frac{7}{8}}$, we need to perform operations in the correct order as per the rules of the order of operations (PEMDAS/BODMAS - Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 1: Simplify the complex fraction $\frac{\frac{10}{7}}{2}$
A complex fraction can be simplified by multiplying the numerator by the reciprocal of the denominator. In this case, the numerator is $\frac{10}{7}$ and the denominator is 2 (which means $\frac{2}{1}$).

$\frac{\frac{10}{7}}{2} = \frac{10}{7} \times \frac{1}{2} = \frac{10 \cdot 1}{7 \cdot 2} = \frac{10}{14}$

Simplify $\frac{10}{14}$ by dividing both the numerator and the denominator by their greatest common divisor (2):

$\frac{10}{14} = \frac{5}{7}$

Step 2: Simplify the complex fraction $\frac{2}{\frac{7}{8}}$
Again, multiply the numerator by the reciprocal of the denominator:
The reciprocal of $\frac{7}{8}$ is $\frac{8}{7}$.

$\frac{2}{\frac{7}{8}} = 2 \times \frac{8}{7} = \frac{2 \cdot 8}{7} = \frac{16}{7}$

Step 3: Add the simplified fractions $\frac{5}{7} + \frac{16}{7}$
Since the fractions have like denominators, we can add the numerators directly:

$\frac{5}{7} + \frac{16}{7} = \frac{5 + 16}{7} = \frac{21}{7}$

Simplify $\frac{21}{7}$ by dividing the numerator by the denominator:

$\frac{21}{7} = 3$

Thus, the solution to the expression is $3$.