Find the real solutions to the equation. \[ \frac{r+1}{r^{2}+15 r+56}=0 \] Real solution(s): \( \{\square\} \)

To solve the equation \[ \frac{r+1}{r^{2}+15r+56}=0, \] we know that a fraction is equal to zero when its numerator is zero (assuming the denominator is not zero). Therefore, we set the numerator equal to zero: \[ r + 1 = 0. \] Solving for \( r \), we get \[ r = -1. \] Next, we need to ensure this value does not make the denominator zero. To check this, we substitute \( r = -1 \) into the denominator \( r^{2} + 15r + 56 \): \[ (-1)^{2} + 15(-1) + 56 = 1 - 15 + 56 = 42. \] Since 42 is not zero, \( r = -1 \) is a valid solution. Therefore, the real solution is \[ \{ -1 \}. \]