Subtracting
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 34 of 54.
Subtracting works like adding, with one trap. Take 4/(x - 2) - 1/(x + 3). Over the common denominator (x - 2)(x + 3), the tops are 4(x + 3) and x - 2, and you take away the whole second top:
4x + 12 - (x - 2) = 4x + 12 - x + 2
So the difference is (3x + 14)/((x - 2)(x + 3)). The fraction bar groups its top the way brackets do, so the minus reaches every term of it, and the minus 2 turns into plus 2. Forget that and you get 3x + 10. Try x = 3 to see which is right: 4/1 - 1/6 is 23/6, the correct top gives 23 over 6, and the wrong one gives 19 over 6.
Challenge
Subtract 5/(x - 1) - 2/(x + 1) and write the result as one fraction.
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 Charts