To solve $(\frac{5}{9} + \frac{5}{6})(\frac{7}{8} + \frac{3}{7})$, follow these steps:

Step 1: Add the fractions inside each parenthesis.

First Parenthesis: $\frac{5}{9} + \frac{5}{6}$

To add these fractions, we need a common denominator. The least common denominator (LCD) of 9 and 6 is 18.

$\frac{5}{9} = \frac{10}{18}, \quad \frac{5}{6} = \frac{15}{18}$

Now, add the fractions:

$\frac{10}{18} + \frac{15}{18} = \frac{25}{18}$

Second Parenthesis: $\frac{7}{8} + \frac{3}{7}$

The LCD of 8 and 7 is 56.

$\frac{7}{8} = \frac{49}{56}, \quad \frac{3}{7} = \frac{24}{56}$

Now, add the fractions:

$\frac{49}{56} + \frac{24}{56} = \frac{73}{56}$

Step 2: Multiply the results of both parentheses.

$\left(\frac{25}{18}\right) \times \left(\frac{73}{56}\right) = \frac{25 \times 73}{18 \times 56} = \frac{1825}{1008}$

Step 3: Simplify the fraction (if possible).

The greatest common divisor (GCD) of 1825 and 1008 is 1, so the fraction cannot be simplified further.

Thus, the final result is:

$\frac{1825}{1008}$

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:

1. How can you simplify a fraction more easily?
2. How do you find the least common denominator (LCD) of two fractions?
3. What are some common ways to check the accuracy of a fraction multiplication?
4. How do you handle mixed numbers in operations like this?
5. Can this fraction be represented as a decimal or percentage?

Tip: Always check if the fractions can be simplified before performing multiplication—it can save time in calculations!