Cross-Multiplying
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 39 of 54.
When each side is a single fraction, there is a shortcut. In 4/(x + 2) = 3/(x - 1), multiply each top by the other side's bottom and set the products equal. This is cross multiplying:
4(x - 1) = 3(x + 2)
Why does it work? It is the same as multiplying both sides by both bottoms, (x + 2)(x - 1). On each side one bottom cancels and the other stays, landing next to the opposite top. It only works when each side is one fraction: 1/x + 2 = 3/x has two terms on the left, so you clear it the long way.
From there it is linear: 4x - 4 = 3x + 6, so x is 10. The bottoms held x, so check it: at 10 neither x + 2 nor x - 1 is 0, and both sides are 1/3.
Challenge
Solve 3/(x + 1) = 2/(x - 1), then check your answer.
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