\( \frac { t } { t + 9 } = \frac { \square } { t ^ { 2 } + 6 t - 27 } \)

To solve this equation, let's first factor the quadratic in the denominator on the right side. The expression \( t^2 + 6t - 27 \) can be factored as \( (t + 9)(t - 3) \). Thus, the equation becomes: \[ \frac{t}{t + 9} = \frac{\square}{(t + 9)(t - 3)} \] To find the value that goes in the box, you can multiply both sides by \( (t + 9)(t - 3) \) to eliminate the fractions: \[ t(t - 3) = \square \] This simplifies to: \[ t^2 - 3t = \square \] Thus, the value that goes in the box is \( t^2 - 3t \).