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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 3x+12=2\frac{3}{x}+\frac{1}{2} = 2, multiply both sides by x. The x cancels from 3x\frac{3}{x}, and the other terms are multiplied by x:

3+x2=2x3+\frac{x}{2} = 2x

The bottom left is a number, cleared as before: times 2 gives 6+x=4x6+x = 4x, so 3x is 6 and x is 2. But something is new. The original equation has no value at x = 0, since 30\frac{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: 32+12\frac{3}{2}+\frac{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.

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Challenge

Solve 2x+13=1\frac{2}{x}+\frac{1}{3} = 1, then check your answer in the original equation.

Try it yourself

2x+13=1\frac{2}{x}+\frac{1}{3} = 1

Get xx alone

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Polynomials & Rational Expressions