Same Bottom
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 32 of 54.
Fractions with the same bottom add the way number fractions do: 2/7 + 3/7 = 5/7. Keep the bottom and add the tops. The same holds with x in them:
(x + 5)/(x + 1) + (2x - 3)/(x + 1) = (x + 5 + 2x - 3)/(x + 1)
Then collect like terms in the top: (3x + 2)/(x + 1). Why keep the bottom? It names the size of the pieces. Both fractions count pieces of the same size, so adding counts pieces, and the size stays as it was. Adding the bottoms would give 2/7 + 3/7 as 5/14, which is smaller than 3/7 alone.
Last, see whether the new top shares a factor with the bottom. (x + 1)/(x + 2) + (x + 3)/(x + 2) gives (2x + 4)/(x + 2), and the top is 2(x + 2), so the whole sum cancels to 2.
Challenge
Add (2x + 1)/(x - 3) + (x - 4)/(x - 3) and write the sum 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