m+4/5m-10+3-m/4m-8

To simplify the expression \( \frac{m + 4}{5m - 10} + \frac{3 - m}{4m - 8} \), we will first factor the denominators where possible.

1. Factor the denominators:

   \[ 5m - 10 = 5(m - 2) \] \[ 4m - 8 = 4(m - 2) \]

So, the expression becomes:

\[ \frac{m + 4}{5(m - 2)} + \frac{3 - m}{4(m - 2)} \]

2. Now, we need a common denominator. The common denominator will be \( 20(m - 2) \), since the least common multiple of \( 5 \) and \( 4 \) is \( 20 \).

3. Rewrite each fraction with the common denominator:

   The first fraction: \[ \frac{m + 4}{5(m - 2)} = \frac{4(m + 4)}{20(m - 2)} = \frac{4m + 16}{20(m - 2)} \]

   The second fraction: \[ \frac{3 - m}{4(m - 2)} = \frac{5(3 - m)}{20(m - 2)} = \frac{15 - 5m}{20(m - 2)} \]

4. Now combine the fractions:

\[ \frac{4m + 16 + 15 - 5m}{20(m - 2)} = \frac{-m + 31}{20(m - 2)} \]

5. Therefore, the simplified form of the expression is:

\[ \frac{31 - m}{20(m - 2)} \]

This is the simplified result of the given expression.