See attached file, please
Hi Alienis,
$\displaystyle \frac{6a^2+2a+20}{4a^2-16}\cdot \frac{10a^2-22a+4}{27a^3-125}$
I'm going to approach this from a different angle. First factor out any common factors in your numerators and denominators.
$\displaystyle \frac{2(3a^2+a+10}{4(a^2-4)}\cdot \frac{2(5a^2-11a+2)}{27a^3-125}$
Next, factor what you have left.
$\displaystyle \frac{2(3a-5)(a+2)}{4(a-2)(a+2)}\cdot \frac{2(5a-1)(a-2)}{(3a-5)(9a^2+15a+25)}$
Now, simplify all you can
$\displaystyle \frac{\rlap{---}2(\rlap{---------}3a-5) \rlap{----------}(a+2)}{\rlap{---}4\rlap{----------}(a-2) \rlap{----------}(a+2)}\cdot \frac{\rlap{---}2(5a-1) \rlap{----------}(a-2)}{\rlap{----------}(3a-5)(9a^2+15a+25)}$
$\displaystyle \frac{5a-1}{9a^2+15a+25}$