Question

The value of $\lim_{𝑥→3}\frac{(𝑥^2 −9)}{(𝑥^2−4𝑥+3 )} $ is (rounded off to the nearest integer).

Answer 1

Correct Answer: 3

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 \(x = 3\):

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