If M = a (m + n) and N=b(m-n), then the value of `(M/a+N/b) div (M/a - N/b)` is:

Answer

To solve the problem, we start with the given expressions for M and N:

1. **Given:**
\[ M = a(m + n) \]
\[ N = b(m - n) \]

2. **We need to find:**
\[ \frac{(M/a + N/b)}{(M/a - N/b)} \]

3. **Substituting M and N:**
- First, let's substitute M and N into the expression:
\[ \frac{(M/a + N/b)}{(M/a - N/b)} = \frac{(a(m+n)/a + b(m-n)/b)}{(a(m+n)/a - b(m-n)/b)} \]

4. **Simplifying the expression:**
- The terms \( a \) in the numerator and denominator of \( M/a \) cancel out, and the terms \( b \) in the numerator and denominator of \( N/b \) also cancel out:
\[ = \frac{(m+n + (m-n))}{(m+n - (m-n))} \]

5. **Further simplification:**
- Now simplify the numerator:
\[ m+n + m-n = 2m \]
- And simplify the denominator:
\[ m+n - (m-n) = m+n - m + n = 2n \]

6. **Final expression:**
- Now we have:
\[ = \frac{2m}{2n} \]
- This simplifies to:
\[ = \frac{m}{n} \]

Thus, the value of \(\frac{(M/a + N/b)}{(M/a - N/b)}\) is \(\frac{m}{n}\).