Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
State restrictions before simplifying a rational expression
Problem
What restrictions apply before simplifying this rational expression? \((x^2~-~1)/(x~-~1)\)
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What this problem is really about
Restrictions belong to the original expression, so determine them before factoring or cancellation. Set each original denominator equal to zero and exclude those solutions; zeros that occur only in numerators are not restrictions. A later cancellation may hide a denominator factor from the simplified formula, but it leaves the corresponding input missing from the domain.
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