Final answer to the problem
Step-by-step Solution
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Factor the difference of squares $9-x$ as the product of two conjugated binomials
Simplify the fraction
Evaluate the limit $\lim_{x\to9}\left(\frac{1}{3+\sqrt{x}}\right)$ by replacing all occurrences of $x$ by $9$
Calculate the power $\sqrt{9}$
Add the values $3$ and $3$
Divide $1$ by $6$