What is a^2-b^2/a-b reduced to its lowest terms.

First, you must figure out another way of writing your numerator, a^2-b^2. You can factor this to (a+b)(a-b); those terms, when multiplied, give you your original numerator, because when you multiply them, the ab terms cancel out (one is positive, one is negative.) You then have

(a+b)(a-b)/a-b

Because your terms in the numerator are multiplied by each other, the a-b terms, one in the numerator and one in the denominator equal one, and you are left with a+b as your answer.