Question

Simplify a^2-3a/a^3-8a^2+12a to lowest terms

Answer 1

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

$a^2-3a = a(a-3)$

At the denominator we have

$a^3-8a^2+12a = a(a^2-8a+12) = a(a-2)(a-6)$

So, the fraction can be written as

$\dfrac{a(a-3)}{a(a-2)(a-6)}$

You can see that there is a factor $a$ in common, that can be simplified:

$\dfrac{a(a-3)}{a(a-2)(a-6)} = \dfrac{a-3}{(a-2)(a-6)}$