We have the following computation, lim x → 4 g ( x ) = lim x → 4 x − 4 x ( x + 4 ) ( x − 4 ) = lim x → 4 1 x ( x + 4 ) = 1 32 {\displaystyle \lim _{x\to 4}g(x)=\lim _{x\to 4}{\frac {x-4}{x(x+4)(x-4)}}=\lim _{x\to 4}{\frac {1}{x(x+4)}}={\frac {1}{32}}} . Notice that, before evaluating the limit, we factored the denominator, and simplified our numerator and denominator.
