Find the domain of f(x)= x-9/x^2-81

The domain will be all real numbers except what makes the denominator of that fraction zero. If the denominator is zero the function is undefined, so it can not be zero.
Two scenarios depending on if parenthesis are missing ..

iff only the x^2 is in the denominator then x is all reals except x ≠ 0.

iff (x^2 - 81) is in the denominator then x is all reals except x ≠ 9 or x ≠ -9.