Rational expression arithmetic

A rational expression is one polynomial divided by another, like (x+1)/(x-2), and you add, subtract, multiply, and divide them the same way you would fractions: for example, 1/x + 1/(x+1) needs a common denominator, x(x+1), giving (x+1)/(x(x+1)) + x/(x(x+1)) = (2x+1)/(x(x+1)), the same idea as 1/2 + 1/3 = 3/6 + 2/6 = 5/6 needing a common denominator of 6; and dividing (1/x) by (x/(x+1)) means flipping and multiplying, (1/x) x ((x+1)/x) = (x+1)/x^2, just like 1/2 divided by 2/3 = 1/2 x 3/2 = 3/4. Just like fractions, rational expressions are closed under these operations, meaning the result of combining two rational expressions is always another rational expression, as long as you avoid dividing by zero.

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