Simplify rational expressions by factoring and identify domain restrictions.
A rational expression is a fraction with polynomials in the numerator and denominator, and it simplifies exactly the way a numeric fraction does: factor top and bottom completely, then cancel any factor that appears in both. The new wrinkle is that a rational expression comes with a DOMAIN -- values of the variable that make the ORIGINAL denominator zero must be excluded, permanently, even if that factor later cancels away.
That last point is worth dwelling on: a cancelled factor does not erase the restriction it came from. If (x+3) cancels out of a fraction, x=-3 still cannot be plugged into the original expression (it would have caused division by zero before any simplifying happened), so the simplified expression is technically only equal to the original everywhere EXCEPT that now-invisible point.
Mastery looks like: They factor and simplify a rational expression correctly and state every domain restriction from the original denominator.
Common stumbles: Canceling individual terms instead of common factors; forgetting a restriction because its factor cancelled during simplification.