12/x+5=-12/5

To solve the equation \( \frac{12}{x} + 5 = -\frac{12}{5} \), follow these steps:

1. Start by isolating the term with \( x \). Subtract 5 from both sides:

   \[ \frac{12}{x} = -\frac{12}{5} - 5 \]

2. To combine the right-hand side, convert 5 into a fraction with a common denominator of 5:

   \[ 5 = \frac{25}{5} \]

   So we have:

   \[ -\frac{12}{5} - \frac{25}{5} = -\frac{12 + 25}{5} = -\frac{37}{5} \]

   Thus, the equation now reads:

   \[ \frac{12}{x} = -\frac{37}{5} \]

3. Cross-multiply to eliminate the fraction:

   \[ 12 \cdot 5 = -37x \]

   This simplifies to:

   \[ 60 = -37x \]

4. Now, solve for \( x \) by dividing both sides by -37:

   \[ x = -\frac{60}{37} \]

So the solution is:

\[ x = -\frac{60}{37} \]