find domain and range of (x²-9)/x-3

the given function is: $f\left(x\right)=\frac{x^2-9}{x-3}$
since the denominator can not be zero.
$$\begin{gathered} x-3\ne 0 \\ \Rightarrow x\ne 3 \end{gathered}$$
the domain of the function is $R-\left\{3\right\}$
$$\begin{gathered} y=f\left(x\right)=\frac{x^2-9}{x-3} \\ y=\frac{(x-3)(x+3)}{x-3} \\ y=x+3 for x\in R-\left\{3\right\} \\ y\ne 3+3 \left[f\right(x) is not defined for x=3 \\ y\ne 6 \end{gathered}$$
range of the function is $R-\left\{6\right\}$

hope this helps you