Compute lim_{x->3} (x^2 - 9)/(x - 3).

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Multiple Choice

Compute lim_{x->3} (x^2 - 9)/(x - 3).

Explanation:
When a limit hits a 0/0 form, simplifying the expression helps reveal the value. The numerator x^2 - 9 is a difference of squares and factors as (x - 3)(x + 3). The expression becomes [(x - 3)(x + 3)]/(x - 3). For x not equal to 3, the (x - 3) factors cancel, leaving x + 3. So the limit as x approaches 3 is the limit of x + 3, which is 6. Direct substitution would give 0/0, which is indeterminate, but the simplification shows the actual limit.

When a limit hits a 0/0 form, simplifying the expression helps reveal the value. The numerator x^2 - 9 is a difference of squares and factors as (x - 3)(x + 3). The expression becomes [(x - 3)(x + 3)]/(x - 3). For x not equal to 3, the (x - 3) factors cancel, leaving x + 3. So the limit as x approaches 3 is the limit of x + 3, which is 6. Direct substitution would give 0/0, which is indeterminate, but the simplification shows the actual limit.

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