Adding rational expressions with common Subtract. \( -\frac{5 a+10 b}{3 a}-\frac{8 a-7 b}{3 a} \) Simplify your answer as much as possible.

To add the rational expressions \(-\frac{5a + 10b}{3a} - \frac{8a - 7b}{3a}\), we can follow these steps: 1. **Combine the numerators**: Since both fractions have the same denominator, we can combine the numerators directly. \[ -\frac{(5a + 10b) + (8a - 7b)}{3a} \] 2. **Distribute the negative sign**: We need to distribute the negative sign across the second numerator. \[ -\frac{5a + 10b + 8a - 7b}{3a} \] 3. **Combine like terms in the numerator**: Now, we can combine the like terms in the numerator. - Combine \(5a\) and \(8a\): \[ 5a + 8a = 13a \] - Combine \(10b\) and \(-7b\): \[ 10b - 7b = 3b \] So, the numerator becomes: \[ 13a + 3b \] 4. **Write the final expression**: Now we can write the combined expression. \[ -\frac{13a + 3b}{3a} \] 5. **Simplify if possible**: The expression \(-\frac{13a + 3b}{3a}\) cannot be simplified further since there are no common factors in the numerator and denominator. Thus, the final simplified answer is: \[ -\frac{13a + 3b}{3a} \]