What does `lim_(x to 2) ((3x^(2)+5)/(x-2))` equal?

Explanation

To solve the limit \( \lim_{x \to 2} \frac{3x^2 + 5}{x - 2} \), we will analyze the behavior of the function as \( x \) approaches 2 from both the right-hand side and the left-hand side.

### Step 1: Define the Right-Hand Limit (RHL)
We will calculate the right-hand limit, which means we will approach \( x = 2 \) from values greater than 2. We can express this as:
\[ \lim_{x \to 2^+} \frac{3x^2 + 5}{x - 2} \]
To make the calculation easier, we substitute \( x = 2 + h \), where \( h \) approaches 0 from the positive side (\( h \to 0^+ \)):
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