Final answer to the problem
$\frac{1}{6}$
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Step-by-step Solution
Specify the solving method
1
Factor the difference of squares $9-x$ as the product of two conjugated binomials
$\frac{3-\sqrt{x}}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}$
2
Simplify the fraction
$\frac{1}{3+\sqrt{x}}$
3
Evaluate the limit $\lim_{x\to9}\left(\frac{1}{3+\sqrt{x}}\right)$ by replacing all occurrences of $x$ by $9$
$\frac{1}{3+\sqrt{9}}$
4
Calculate the power $\sqrt{9}$
$\frac{1}{3+3}$
5
Add the values $3$ and $3$
$\frac{1}{6}$
6
Divide $1$ by $6$
$\frac{1}{6}$
Final answer to the problem
$\frac{1}{6}$
Exact Numeric Answer
$0.1667$