One True, One False
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 41 of 54.
Solve x^2/(x + 3) = 9/(x + 3). Multiply both sides by x + 3: x^2 = 9. Take the square root of both sides, and there are two candidates: x = 3 or x = -3.
Check each one in the original. At 3, the bottom is 6, and both sides are 9/6: it stands. At -3, the bottom is 0: it is extraneous and goes. The solution is x = 3 only. One false answer does not spoil the others, because it comes from one particular value making a bottom 0.
So check every candidate on its own, and throw out only the ones that make a bottom 0.
Challenge
Solve x^2/(x - 2) = 4/(x - 2). Check each candidate in the original equation.
Try it yourself
Solve for x
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 Charts8Rational Equations
Clearing Fractionsx in the BottomCross-MultiplyingA False AnswerOne True, One FalseRecap: Rational Equations