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Add and Subtract Rational Expressions

Same Denominator

Simplify[(x + 1)/(x - 2) + (2x - 3)/(x - 2)]

Different Denominators

Simplify[(1/x) + (2/(x + 1))]

More:

Simplify[(x + 2)/(x^2 - 1) - (x - 1)/(x^2 - 1)]

What is the common denominator? How does CAS help students confirm or discover the correct procedure?