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