posted by jan .
((5a^2+12a+4)/(a^4-16)) / ((25a^2+20a+4)/(a^2-2a))
Factor each of the four terms in parentheses and see which factors you can cancel out. This is not hard. Surely you can factor
a^4 - 16 and a^2 -2a
5a^2 + 12a +4 = (5a +2)(a + 2)
25a^2 +20a +4 = (5a +2)(5a + 2)
Now put it all together