Hint: Try expanding everything else so that you have expression in the numerator and one in the denominator.
Once you have that, look for a way to factorize expressions and cancel things out.
Lets look at b)
2x/(x^3 +x^2 - 6x) - (x-8)/(x^2 - 5x - 24)
= 2x/[x*(x^2 + x - 6)] - (x-8)/[(x-8)(x+3)]
= 2/[x^2 + x - 6] - 1/(x+3)
= 2/[(x+3)(x-2)] - 1/(x+3)
= 2/[(x+3)(x-2)] - (x-2)/[(x-2)(x+3)]
= (4 - x)/[(x+3)(x-2)] (since 2 - x + 2 = 4 - x).
It's not , I can see you're trying to apply a rule without really understanding what's going on (and messing up the numerator).
To add two fractions, you need a common denominator. In the first your denominator is 2, and in the second your denominator is t. So the common denominator is 2t. Whatever you do to the bottom of each fraction to get the common denominator, you need to do to the top as well. You're really multiplying each fraction by a cleverly disguised 1, because when you multiply by 1, your number remains the same. So