We can find the answer by replacing every occurrence of x with 9 in the given expression as shown below.
[tex] \frac{ x^{2} +6}{x-6} \\ \\
= \frac{9^{2}+6 }{9-6} \\ \\
= \frac{81+6}{3} \\ \\
= \frac{87}{3} \\ \\
=29[/tex]
So, the value of expression at x=9 is 29
