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3 Responses
Rule of thumb: you can only cancel factors, not terms-if there’s a + or −, factor first (or distribute to line things up) and then cancel. Example: (6x^2+12x)/(3x) = 3x(2x+4)/(3x) → 2x+4 (don’t cancel the x in x+2); quick refresher: https://www.khanacademy.org/math/algebra/rational-expressions-equations/simplify-rational-expressions/a/simplifying-rational-expressions-review
Great rule of thumb: you’re only allowed to cancel factors, not terms. Think of a fraction like a sandwich wrapped in parentheses-if the same “wrapper” (a factor) is multiplying the whole top and the whole bottom, you can peel it off both. For example, (x²−9)/(x−3) isn’t ready to cancel yet because there’s subtraction; but once you factor the top as (x−3)(x+3), then the (x−3) is a full‑blown factor and you can cancel it (as long as x≠3). Same with x(x+3)/(x+3) → x, but not with (x+3)/x (no common factor). If you see plus or minus signs, try factoring first; if you see products, cancelling common factors is fair game. Distribute when you need to remove parentheses to combine like terms (e.g., 3(x+2)=3x+6), but avoid distributing in a fraction if factoring would let you cancel something cleanly. Quick check: if something only matches part of a sum, you can’t cancel; if it multiplies the whole top and bottom, you can. And always remember the domain-any cancelled factor that could be zero is still excluded. Hope this helps!
Quick compass: you can cancel only common factors-things multiplying the entire numerator and denominator-never pieces trapped inside a + or −; if there’s addition/subtraction, factor first to reveal a product (or distribute only to combine like terms), then cancel, keeping excluded denominator values in mind. Analogy: +/− are little fences and × are gates-matching sheep can exit through gates, not hop the fences.