Question:

The value of $\lim_{π‘₯β†’3}\frac{(π‘₯^2 βˆ’9)}{(π‘₯^2βˆ’4π‘₯+3 )} $ is (rounded off to the nearest integer).

Updated On: Mar 23, 2025
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Correct Answer: 3

Solution and Explanation

Factorize both the numerator and denominator:

\( x^2 - 9 = (x - 3)(x + 3), \)

\( x^2 - 4x + 3 = (x - 3)(x - 1). \)

So, the expression becomes:

\( \frac{(x - 3)(x + 3)}{(x - 3)(x - 1)}. \)

Cancel out the \((x - 3)\) terms:

\( \frac{x + 3}{x - 1}. \)

Substitute \(x = 3\):

\( \frac{3 + 3}{3 - 1} = \frac{6}{2} = 3. \)

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