What should be added to `((2)/(3)+(3)/(5))` to get `(-2)/(15)`?

Answer

To solve the problem, we need to find out what should be added to \(\frac{2}{3} + \frac{3}{5}\) to get \(-\frac{2}{15}\). Let's go through the steps systematically.

### Step 1: Set up the equation
Let \(x\) be the number that we need to add. We can write the equation as:
\[ \frac{2}{3} + \frac{3}{5} + x = -\frac{2}{15} \]

### Step 2: Isolate \(x\)
To find \(x\), we can rearrange the equation:
\[ x = -\frac{2}{15} - \left(\frac{2}{3} + \frac{3}{5}\right) \]

### Step 3: Calculate \(\frac{2}{3} + \frac{3}{5}\)
To add \(\frac{2}{3}\) and \(\frac{3}{5}\), we need a common denominator. The least common multiple (LCM) of 3 and 5 is 15.

Convert each fraction:
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

Now add them:
\[ \frac{10}{15} + \frac{9}{15} = \frac{10 + 9}{15} = \frac{19}{15} \]

### Step 4: Substitute back into the equation for \(x\)
Now substitute \(\frac{19}{15}\) back into the equation for \(x\):
\[ x = -\frac{2}{15} - \frac{19}{15} \]

### Step 5: Combine the fractions
Since both fractions have the same denominator, we can combine them:
\[ x = \frac{-2 - 19}{15} = \frac{-21}{15} \]

### Step 6: Simplify the fraction
Now simplify \(\frac{-21}{15}\):
\[ x = \frac{-21 \div 3}{15 \div 3} = \frac{-7}{5} \]

### Conclusion
Thus, the value that should be added to \(\frac{2}{3} + \frac{3}{5}\) to get \(-\frac{2}{15}\) is:
\[ \boxed{-\frac{7}{5}} \]