Determine where the function \( m(x)=\frac{x+6}{(x-6)(x-2)} \) is continuous.

To determine where the function \( m(x)=\frac{x+6}{(x-6)(x-2)} \) 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 \((x-6)(x-2)\). The function is not defined when the denominator is equal to zero, so we need to find the values of \( x \) that make the denominator zero. Setting the denominator equal to zero and solving for \( x \): \((x-6)(x-2) = 0\) This equation is satisfied when \( x = 6 \) or \( x = 2 \). Therefore, the function is not continuous at \( x = 6 \) and \( x = 2 \). The function is continuous for all other values of \( x \) except at \( x = 6 \) and \( x = 2 \).