1. how do u simplify (1/a+h+1 - 1/a+1)/h

2.what's the difference quotient? is it like what u start with e.g. f(x)=1/x+1 or is it the big equation ur suppose to plug it into eg. f(a+h)-f(a)/h or is it what u plug into the f(x)=1/x+1 to get for e.g. f(a)/a+1?

1. What you have in the numerator can be rewritten h+2. This can be rewritten 1 + (2/h)

I am assuming that your 1/a terms are individual terms, which cancel out, and that you did intend mean to write
1/(a+h+1) nor 1(a+h) + 1

2. I expect that by "difference quotient" they mean [f(a+h)-f(a)]/h

You need to be more precise in your use of parentheses and brackets. Many of the expressions you have written are ambiguous, and can be interpreted in various ways that are not the same.