$g '\left( a \right)=\lim_{t \rightarrow a} \left(\frac{ \frac{ 3 }{ t-4 }-\frac{ 3 }{ a-4 } }{ t-a }\right)$
Evaluate the limit$g '\left( a \right)=-\frac{ 3 }{ {a}^{2}-8a+16 }$
The initial variable is $t$, so substitute $t$ for $a$$g '\left( t \right)=-\frac{ 3 }{ {t}^{2}-8t+16 }$
Use ${a}^{2}-2ab+{b}^{2}={\left( a-b \right)}^{2}$ to factor the expression$g '\left( t \right)=-\frac{ 3 }{ {\left( t-4 \right)}^{2} }$