What is the limit? limit x to 5 of the fraction with numerator square root of x plus 4 end root minus 3 and denominator x minus 5

Direct substitution gives 0/0, so rationalize the numerator by multiplying by √(x + 4) + 3. The expression simplifies to 1/(√(x + 4) + 3), which approaches 1/(3 + 3) = 1/6 as x approaches 5; the correct choice is one sixth.

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