Multiply and Divide Rational Expressions

CAS Simplification
[br][br]Try:[br][br][b]Simplify[(x^2 - 4)/(x + 2)][/b][br][br][br]Then:[br][br][b]Simplify[((x^2 - 4)/(x + 2)) * (x + 2)/(x + 3)][/b][br][br]
[b]Why does the result simplify this way? What terms cancel?[/b]
[br][br][br][br]--[br][br][br][br]
Try some Non-Trivial Factorizations
[br][br][b]Simplify[((x^2 + 5x + 6)/(x^2 - 1)) * ((x - 1)/(x + 2))][/b][br]
[b]How does CAS handle common factors?[br]Could this be used to verify student work?[/b][br]
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Information: Multiply and Divide Rational Expressions