For context: We have been working with the concept of limits in my Math 170 class. I understand what a Limit is quite well, but I am struggling with some of the algebra associated with finding limits. Here are two problems i'm having trouble with.

1)The limit as x approaches -4 of (1/4 + 1/x) / (4+x)

2)The limit as t approaches 0 of (sqrt(1+t) - sqrt(1-t)) / t

These both seem to me to be simple, but when I try and simplify I seem to just work myself in circles, never able to reach a point in which I can use the limit law for quotients.

Thanks for any help you may have.