In order to simplify a fraction, we have to find a common factor in both numerator and denominator. So, let's start by factor the expressions completely: at the numerator we have
[tex] a^2-3a = a(a-3) [/tex]
At the denominator we have
[tex] a^3-8a^2+12a = a(a^2-8a+12) = a(a-2)(a-6) [/tex]
So, the fraction can be written as
[tex] \dfrac{a(a-3)}{a(a-2)(a-6)} [/tex]
You can see that there is a factor [tex] a [/tex] in common, that can be simplified:
[tex] \dfrac{a(a-3)}{a(a-2)(a-6)} = \dfrac{a-3}{(a-2)(a-6)} [/tex]
