One I am having trouble with...

I assume here that 999^s is wrong, instead it is 999^2

Here is how I solved it

[(1000+1)^2 - (1000-1)^2]/[(100+1)^2 - (100-1)^2]

you end up with 4000/400 = 10

However I would like to know if there is a easier way to solve this?

First things first .. this should be in the PS section .. so moved to the PS section

An easier way to solve this is to use the formula (a^2-b^2) = (a-b)(a+b)

So, 1001^2-999^2 = (1001+999)(1001-999) = 2000*2 and 101^2-99^2 = (101+99)(101-99) = 200*2

Therefore (1001^2-999^2)/(101^2-99^2) = 4000/400 = 10 ..

Thanks Gabriel! I should have gotten that one!

Thanks for moving it as well!