Cancel factors, never terms
SAT glossary · Course Foundations
Definition
Rational expressions simplify only by factoring: ((x+3)(x-3))/((x+3)(x+2))=(x-3)/(x+2). You may never cancel terms — (x+3)/(x+2)≠frac32 — because x+3 is a sum, not a product, and cancellation is division, and you cannot divide part of a sum.
Cancel factors, never terms in plain English
A rational expression is basically a fraction where the top and bottom are made of algebra instead of plain numbers, like ((x+3)(x-3))/((x+3)(x+2)). You're only allowed to cancel out FACTORS — pieces that are being multiplied together — never a piece that's just sitting inside a sum. In the example above, (x+3) appears as a multiplied factor on both top and bottom, so it's legal to cancel it, leaving (x-3)/(x+2). But you could never do something like canceling the 'x' out of (x+3)/(x+2) to get 3/2 — that's illegal, because x+3 is an ADDITION, not a multiplication, and you can't just chop a piece out of a sum. Cancellation is really division, and you can only divide out something that's multiplying the WHOLE top and the WHOLE bottom.
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