x in the Bottom
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 35 of 51.
When x sits in a bottom, clear it the same way: multiply by the bottom. In , multiply both sides by x. The x cancels from , and the other terms are multiplied by x:
The bottom left is a number, cleared as before: times 2 gives , so 3x is 6 and x is 2. But something is new. The original equation has no value at x = 0, since means nothing. Multiplying by x is only safe when x is not 0, so an answer must be checked in the original equation: is 2, so x = 2 stands.
Once x stands alone, the board asks you to check it: tap Check x = 2 in the original equation.
Challenge
Solve , then check your answer in the original equation.
Try it yourself
Get alone
This 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 WorksThe Remainder TheoremA Missing TermRecap: Long Division7Adding and Subtracting
Same BottomDifferent BottomsSubtractingFactor the Bottoms FirstRecap: Adding Fractions2Remainders and Factors
The Factor TheoremFinding a Missing NumberUsing a Known FactorRecap: Remainders and Factors5Sign Charts
Between the RootsOutside the RootsA Negative Leading TermReading a Sign ChartRecap: Sign Charts8Rational Equations
Clearing Fractionsx in the BottomCross-MultiplyingA False AnswerOne True, One FalseRecap: Rational Equations