Multiply or divide rational expressions by factoring first, cancelling across numerator/denominator pairs, then simplifying. Includes all domain restrictions from original denominators.
(A/B) × (C/D) = AC / BD
Always factor every numerator and denominator completely before multiplying. Once everything is factored, you can cancel any factor in a numerator with the same factor in any denominator — not just the ones in the same fraction.
Example: (x+2)/(x−1) × (x²−1)/(x+2) — factor x²−1 = (x+1)(x−1), then cancel (x+2) top/bottom and (x−1) top/bottom to get (x+1)/1 = x+1.
Cross-cancelling before multiplying keeps numbers small and avoids expanding unnecessarily.
(A/B) ÷ (C/D) = (A/B) × (D/C)
"Keep, Change, Flip" — keep the first fraction unchanged, change the ÷ to ×, and flip (take the reciprocal of) the second fraction. Then follow the same multiply steps: factor, cross-cancel, simplify.
Domain warning: For division, the numerator of the second fraction also becomes a denominator after flipping — so its zeros are additional restrictions on the domain, even if they cancel out.
One-on-one Algebra 2 tutoring makes rational expressions click — we work through your actual problems and build the pattern recognition that sticks for tests and beyond.