x in the Bottom
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 38 of 54.
When x sits in a bottom, clear it the same way: multiply by the bottom. In 3/x + 1/2 = 2, multiply both sides by x. The x cancels from 3/x, and the other terms are multiplied by x:
3 + x/2 = 2x
The bottom left is a number, cleared as before: times 2 gives 6 + x = 4x, so 3x is 6 and x is 2. But something is new. The original equation has no value at x = 0, since 3/0 means nothing. Multiplying by x is only safe when x is not 0, so an answer must be checked in the original equation: 3/2 + 1/2 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 2/x + 1/3 = 1, then check your answer in the original equation.
Try it yourself
Solve for x
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 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 Charts8Rational Equations
Clearing Fractionsx in the BottomCross-MultiplyingA False AnswerOne True, One FalseRecap: Rational Equations