What is the limit? limit x to 3 of the fraction with numerator square root of x plus 1 end root minus 2 and denominator x minus 3

Direct substitution gives 0/0, so rewrite the fraction by multiplying the numerator and denominator by the conjugate, √(x + 1) + 2. This simplifies it to 1/(√(x + 1) + 2) for x ≠ 3. As x approaches 3, this expression approaches 1/(2 + 2) = 1/4, so the answer is D, one fourth.

AI-written and checked against the verified answer.