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comment $-1$ is not $ 1$, so where is the mistake?
@frogeyedpeas: There are plenty of alternative ways in which one can define the radical sign and/or the numbers, but keep in mind that the context here is algebra-precalculus, so these things have a fairly standard definition.
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comment Find a set of generators and relations for $S_3$
@LeslieFaulkner: When you posted your math questions on the meta site twice, there was a large box to the right of the title space that said in large letters, "Is your question about the Mathematics Stack Exchange community or website?" Your questions weren't. As a new user, you might want to make sure that you read at least the things in large bold type and pay attention to them before telling the longer-time users that they're being rude.
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revised Prove the following trigonometric identity.
TeX tweaks
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comment Prove the following trigonometric identity.
I wouldn't call this rationalizing the denominator, as there's nothing necessarily rational or irrational about the denominator before or after the initial multiplication, but this technique does mirror the technique for rationalizing denominators: using conjugates.