3а-4б/а + 8а2+4б2 /аб

To simplify the expression \( \frac{3a - 4b}{a} + \frac{8a^2 + 4b^2}{ab} \), we can break this down step by step.

1. Simplify the first term: \[ \frac{3a - 4b}{a} = \frac{3a}{a} - \frac{4b}{a} = 3 - \frac{4b}{a} \]

2. Simplify the second term: \[ \frac{8a^2 + 4b^2}{ab} = \frac{8a^2}{ab} + \frac{4b^2}{ab} = \frac{8a}{b} + \frac{4b}{a} \]

3. Combine the simplified terms: Now, we add the two simplified terms together: \[ 3 - \frac{4b}{a} + \frac{8a}{b} + \frac{4b}{a} \] Notice that \( -\frac{4b}{a} + \frac{4b}{a} = 0 \).

4. Final expression: Therefore, the expression simplifies to: \[ 3 + \frac{8a}{b} \]

Thus, the fully simplified form of the original expression is:

\[ 3 + \frac{8a}{b} \]