Simplify ((4a+4)/(3a-12)*(a^2-6a+8)/(a^2+3a-4))÷((4a-12)/(3a+12))

Factor ${\displaystyle 4}$ out of ${\displaystyle 4a+4}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3a-12}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 8}$ and whose sum is ${\displaystyle -6}$.

Write the factored form using these integers.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -4}$ and whose sum is ${\displaystyle 3}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle a-4}$.

Multiply ${\displaystyle \frac{4(a+1)}{3}}$ by ${\displaystyle \frac{a-2}{(a-1)(a+4)}}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3a+12}$.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4a-12}$.

Cancel the common factor of ${\displaystyle 4}$.

Cancel the common factor of ${\displaystyle 3(a+4)}$.

Multiply ${\displaystyle \frac{(a+1)(a-2)}{a-1}}$ by ${\displaystyle \frac{1}{a-3}}$.