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Let's solve the given limit problem step by step. The expression is:

\[
\lim_{{x \to 3}} \frac{x^2 - 7}{3 - x}
\]

### Step 1: Factor the numerator (if possible)

The numerator is \( x^2 - 7 \), which doesn't factor nicely. So, we move on to evaluating the limit directly.

### Step 2: Substituting \( x = 3 \)

Substituting \( x = 3 \) directly into the expression:

\[
\frac

Use the Theorem on Limits of Rational Functions to find the limit. lim x→3 (x^2 - 7)/(3 - x)

Find the limit of the rational function (x^2 - 7) / (3 - x) as x approaches 3. The problem involves the theorem on limits of rational functions and requires simplification to find the answer.

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