Question 178268
If you remember, when you are multiplying two binomials, you can use a mind trick called FOIL (first, outside, inside, last).  Just in case you haven't heard this before, it means multiply the two first terms of each binomial, then the two outside terms, then the two inside terms, and finally, the two last terms.  So, for
{{{(sqrt(n+1)+sqrt(n))(sqrt(n+1)-sqrt(n))}}}
So, once we FOIL, we get
{{{sqrt(n+1)sqrt(n+1) - sqrt(n+1)sqrt(n) + sqrt(n)sqrt(n+1) -sqrt(n)sqrt(n)}}}
Now, simplifying (remember that sqrt(x)sqrt(x)=x) we get
{{{n+1-n}}}
{{{1}}}
So, oddly enough, that entire expression simplifies to just 1.  Doesn't that just annoy you? :)