Multiplying
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 29 of 54.
Multiplying rational expressions works like (2/3) × (9/4): multiply the tops, multiply the bottoms, then cancel. Take ((x^2 - 4)/(3x)) × ((6x)/(x - 2)). Factor first, so the shared factors are in plain view: x^2 - 4 is (x + 2)(x - 2). Then multiply across:
((x + 2)(x - 2) × 6x)/(3x(x - 2))
Now cancel every factor the top and bottom share: x - 2 goes, x goes, and 6 over 3 leaves 2. What remains is 2(x + 2), and multiplying out the top gives the finished answer, 2x + 4. There is no common denominator to find: that is only needed when you add or subtract.
The excluded values still come from the original bottoms: here 0 and 2, even though both cancelled.
Challenge
Multiply and simplify ((x^2 - 1)/(2x)) × ((4x)/(x + 1)). Write the answer with its top multiplied out.
Try it yourself
Write it as one fraction
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Polynomials & Rational Expressions
1Polynomial Long Division
How Long Division WorksOne Term at a TimeA Remainder Left OverA Missing TermDividing by a QuadraticRecap: Long Division7Adding and Subtracting
Same BottomDifferent BottomsSubtractingFactor the Bottoms FirstRecap: Adding Fractions2Remainders and Factors
The Remainder TheoremThe Factor TheoremFinding a Missing NumberUsing a Known FactorRecap: Remainders and Factors5Sign Charts
Between the RootsOutside the RootsA Negative Leading TermReading a Sign ChartRecap: Sign Charts3Factoring Higher Degree
Factor by GroupingGrouping All the WayDifference of CubesSum of CubesA Quadratic in DisguiseRecap: Factoring6Rational Expressions
Cancelling FactorsExcluded ValuesMultiplyingDividingRecap: Rational Expressions