Find the sum:
`(-8)/(19) + ((-2))/(57)`

Answer

To find the sum of the rational numbers \(-\frac{8}{19}\) and \(-\frac{2}{57}\), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Rational Numbers**:
We have two rational numbers:
\[ -\frac{8}{19} \quad \text{and} \quad -\frac{2}{57} \]

2. **Combine the Signs**:
Since we are adding a negative number to another negative number, we can write:
\[ -\frac{8}{19} + (-\frac{2}{57}) = -\frac{8}{19} - \frac{2}{57} \]

3. **Find a Common Denominator**:
The denominators are 19 and 57. To add these fractions, we need a common denominator. The least common multiple (LCM) of 19 and 57 is 57 (since 57 is a multiple of 19).

4. **Convert the First Fraction**:
We need to convert \(-\frac{8}{19}\) to have a denominator of 57. We can do this by multiplying both the numerator and the denominator by 3:
\[ -\frac{8}{19} = -\frac{8 \times 3}{19 \times 3} = -\frac{24}{57} \]

5. **Rewrite the Expression**:
Now we can rewrite the expression with a common denominator:
\[ -\frac{24}{57} - \frac{2}{57} \]

6. **Combine the Numerators**:
Now that the denominators are the same, we can combine the numerators:
\[ -\frac{24 + 2}{57} = -\frac{26}{57} \]

7. **Final Answer**:
The final answer is:
\[ -\frac{26}{57} \]