12/х+5 = - 12/5

To solve the equation \( \frac{12}{x} + 5 = -\frac{12}{5} \), follow these steps: 1. **Isolate the fraction**: \[ \frac{12}{x} = -\frac{12}{5} - 5 \] To combine the terms on the right side, we need a common denominator. Rewrite 5 as a fraction: \[ 5 = \frac{25}{5} \] Now we can express the right side: \[ -\frac{12}{5} - \frac{25}{5} = -\frac{12 + 25}{5} = -\frac{37}{5} \] Now the equation becomes: \[ \frac{12}{x} = -\frac{37}{5} \] 2. **Cross-multiply**: \[ 12 \cdot 5 = -37 \cdot x \] \[ 60 = -37x \] 3. **Solve for \( x \)**: Divide both sides by -37: \[ x = -\frac{60}{37} \] So the solution to the equation is: \[ x = -\frac{60}{37} \]