Cancel with Care
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 57 of 64.
In (4x^2 + 2x)/(2x), you cannot cross out the 2x on top against the 2x below and leave the rest alone. The denominator divides the whole sum, not one term of it.
Divide each term by 2x: 4x^2/(2x) = 2x and 2x/(2x) = 1, for nonzero x. The quotient is 2x + 1. A nonzero expression divided by itself is 1, so the second term becomes 1. It does not disappear.
You may cancel a factor that is shared by the whole numerator and the whole denominator. You may not cancel one term inside a sum. If you factor the numerator as 2x(2x + 1), then 2x is a factor of the whole top, and you can cancel it. Cancelling leaves 2x + 1, for nonzero x.
Challenge
MediumDivide: (9x^2 + 3x)/(3x). The second term divides to 1, and the 1 stays in the answer.
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