Answer :
Given rational expression is
[tex]\frac{t^2-4}{6t-12}[/tex]Factor the numerator and denominator first.
[tex]\begin{gathered} t^2-4=t^2-2^2 \\ =(t+2)(t-2) \end{gathered}[/tex]Factor the denominator 6t-12:
[tex]\begin{gathered} 6t-12=6t-6\cdot2 \\ =6(t-2) \end{gathered}[/tex]So,
[tex]\begin{gathered} \frac{t^2-4}{6t-12}=\frac{(t+2)(t-2)}{6(t-2)} \\ =\frac{t+2}{6} \end{gathered}[/tex]Therefore, the given expression in lowest form is
[tex]\frac{t+2}{6}[/tex]