Determine where the function \( m(x)=\frac{x+3}{(x-3)(x-6)} \) is continuous.

To determine where the function \( m(x)=\frac{x+3}{(x-3)(x-6)} \) is continuous, we need to find the values of \( x \) for which the function is defined and continuous. The function is continuous at all points where the denominator is not equal to zero, as division by zero is undefined. The denominator of the function is \((x-3)(x-6)\). The function is not defined when the denominator is equal to zero, which occurs when \( x = 3 \) or \( x = 6 \). Therefore, the function is continuous for all real numbers except \( x = 3 \) and \( x = 6 \).