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Question
\[\lim_{x \to 3} \left( \frac{1}{x - 3} - \frac{3}{x^2 - 3x} \right)\]
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Solution
\[\lim_{x \to 3} \left[ \frac{1}{x - 3} - \frac{3}{x^2 - 3x} \right]\]
\[ = \lim_{x \to 3} \left[ \frac{1}{x - 3} - \frac{3}{x\left( x - 3 \right)} \right]\]
\[ = \lim_{x \to 3} \left[ \frac{x - 3}{x\left( x - 3 \right)} \right]\]
\[ = \lim_{x \to 3} \left[ \frac{1}{x} \right]\]
\[ = \frac{1}{3}\]
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