Cancel with Care
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 57 of 64.
The most tempting illegal move in algebra lives on this page. In (4x^2 + 2x)/(2x), the eye sees 2x above and 2x below and wants to strike out the pair, leaving 4x^2. That move is wrong, and the correct answer shows why.
Split honestly: 4x^2/(2x) = 2x and 2x/(2x) = 1. The quotient is 2x + 1. The term that "cancelled" did not vanish; it became 1, because 2x/(2x) is a number divided by itself.
The law: cancellation strikes factors of the whole top and bottom, never a lone term of a sum. Factored, 2x(2x + 1) over 2x cancels legally to 2x + 1: same answer, both roads honest.
Challenge
MediumDivide: (9x^2 + 3x)/(3x). The matching term does not vanish.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative