Algebra 2: 4 Rational expressions problems - help/check my work?

Hi, I'm really struggling with a worksheet, I was wondering if someone could check my work and explain where i went wrong so i understand how to do it in the future- Thanks

Simplify:

Problem #1:

3a^2 - 24a

---------------

3a^2 + 12a

I got:

a-8

-----

a+4

by canceling 3a out of 3a^2 and 12a and also by canceling 3a out of -24a and 3a^2

Problem #2:

(5s^2 / s^2 - 4) * (s + 2/10s^2)

for this i got: 1/(s-2)(2s^3) by canceling 5s^2 from 5s^2 and 10s^5 and by canceling s+2 from s+2 and s^2 - 4

Problem #3:

(q^2 + 2q / 6q ) * (q^2 - 4 / 3q^2)

For this.. i made it (q^2 + 2a)/6q * (3q^2)/(q^2 - 4) by multiplying by the reciprocal

I canceled out q^2 from q^2 + 2a and from q^2 - 4

I also canceled out 3q from 6q and 3q^2

which gave me 6a/-2 or -3a

Lastly, Problem #4:

(t^2 + 19t + 84 / 4t-4) * (2t - 2 / t2 + 9t + 14)

I factored out: t^2 + 19t + 84 and got (t + 7)(t+ 12)

and i also factored out t^2 + 9t + 14 and got (t + 2)(t+7)

both factored by MARFing

This made the problem:

(t+7)(t + 12) / 4t - 4 * (2t - 2)/ (t+2)(t+7)

I canceled out the t+7 and this left me with...

(2t - 2)(t + 12) / (4t - 4)(t+2)

I wasnt sure if i could reduce/cancel out further....

Thanks :P