Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Multiply rational expressions and preserve original-domain restrictions
Problem
Multiply and simplify \((x^2~-~1)/(x~+~2)\) times \((x~+~2)/(x~-~1)\). State all restrictions from the original expression.
Big Picture
What this problem is really about
For a product of rational expressions, preserve the domain before simplifying. List zeros of every original denominator, factor all polynomials, and view the entire multiplication as one numerator over one denominator. Cancel only identical whole factors across that overall fraction, then carry the original denominator exclusions forward without adding zeros that came only from numerators.
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