Use algebra and the properties of limits as needed to find the given limits. If the limit does not exist, say so. \( \lim _{x \rightarrow-2} \frac{(x+2)^{2}(x-7)}{(x-2)(x+2)^{2}} \)

To find the limit \( \lim _{x \rightarrow-2} \frac{(x+2)^{2}(x-7)}{(x-2)(x+2)^{2}} \), we first notice that the \( (x + 2)^2 \) terms in the numerator and denominator cancel out because they can be factored out. This simplifies our limit to: \[ \lim _{x \rightarrow-2} \frac{x - 7}{x - 2} \] Now, substituting \( x = -2 \): \[ \frac{-2 - 7}{-2 - 2} = \frac{-9}{-4} = \frac{9}{4} \] So, the limit is: \[ \frac{9}{4} \]