To find where the rational expression \(\frac{y - 6}{y^2 + 9}\) is undefined, we need to determine where the denominator is equal to zero since a rational expression is undefined at those points.
The denominator of the given expression is \(y^2 + 9\). We set it equal to zero:
\[ y^2 + 9 = 0 \]
To solve for \(y\), we rearrange this equation:
\[ y^2 = -9 \]
Taking the square root of both sides, we get:
\[ y = \pm \sqrt{-9} = \pm 3i \]
This indicates that \(y = 3i\) and \(y = -3i\) are the points where the expression is undefined. Since these are complex numbers, it means that the rational expression is defined for all real numbers and is only undefined for these specific complex values.
Thus, the expression \(\frac{y - 6}{y^2 + 9}\) is undefined at:
\[ y = 3i \quad \text{and} \quad y = -3i \]