Factor the Bottoms First
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 35 of 54.
Take 2/(x^2 - 25) + 1/(x - 5). Multiplying the bottoms would give a cubic, far more than you need. Factor first: x^2 - 25 = (x + 5)(x - 5). Now you can see that the second bottom, x - 5, is already inside the first.
So the least common denominator is just (x + 5)(x - 5). The first fraction already has it, and the second is only missing x + 5:
2/((x + 5)(x - 5)) + (x + 5)/((x + 5)(x - 5))
Why factor? A common denominator is built from factors: every factor of every bottom must be in it, and nothing more. Shared factors only show once the bottoms are factored. Adding the tops gives (x + 7)/((x + 5)(x - 5)).
Challenge
Add 3/(x^2 - 4) + 1/(x + 2) and write the sum as one fraction. Factor the first bottom before anything else.
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