Dividing by a Variable Term
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 55 of 64.
When the divisor contains x, split the fraction in the same way. Then use the quotient rule on each piece: divide the coefficients and subtract the exponents. For (6x^2 + 9x)/(3x), the pieces are 6x^2/(3x) = 2x and 9x/(3x) = 3.
The quotient is 2x + 3. Look at the second term. In 9x/(3x), the x on top and the x below cancel, because x/x = 1. Only the number 3 is left. A term loses its x completely when the divisor has the same power of x.
There is a second method. Factor the numerator as 3x(2x + 3), then cancel the common factor 3x from the top and the bottom, for nonzero x. Both methods give 2x + 3. The next section explains how to factor polynomial expressions.
Challenge
MediumDivide: (12x^2 + 8x)/(4x).
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