Different Bottoms
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 33 of 54.
To add 1/2 + 1/3, you first rewrite both over 6: 3/6 + 2/6, which is 5/6. The pieces must be the same size before you can count them. The smallest bottom both 2 and 3 go into, 6, is the least common denominator.
Fractions with x work the same way. In 3/x + 1/(x + 4), the bottoms x and x + 4 share no factor, so the least common denominator is their product, x(x + 4). Each fraction is multiplied top and bottom by the factor it is missing: the first by x + 4, the second by x.
(3(x + 4))/(x(x + 4)) + x/(x(x + 4))
Multiplying top and bottom by the same nonzero thing multiplies the fraction by 1, so its value does not change. Now add the tops and collect: (4x + 12)/(x(x + 4)). Leave the bottom factored, so you can see at a glance that nothing cancels.
Challenge
Add 2/x + 3/(x + 2) 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