Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Simplify a complex rational expression with all restriction sources
Problem
Simplify \((1/x~+~1/y)/(1/x)\) and state its complete original domain.
Big Picture
What this problem is really about
A complex fraction has restrictions hidden at two levels. First require every inner denominator to be nonzero, then check whether the entire expression in the main denominator can equal zero. After recording that full domain, multiply the top and bottom by a common denominator that clears every small fraction, and simplify the resulting ordinary fraction.
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