Evaluate `lim_(xto-3) (x^(3)+27)/(x^(5)+243)`

Explanation

To evaluate the limit \( \lim_{x \to -3} \frac{x^3 + 27}{x^5 + 243} \), we can follow these steps:

### Step 1: Identify the form of the limit
First, we substitute \( x = -3 \) into the expression:
\[ x^3 + 27 = (-3)^3 + 27 = -27 + 27 = 0 \]
\[
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