Rational and Radical Equations Flashcard

Front

Define a rational equation.

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and denominator are polynomials.

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What is an extraneous solution in the context of rational equations?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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Back

x=1

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x=3

Front

What is the first step in solving a rational equation?

Back

The first step is to find a common denominator to eliminate the fractions.

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x=4

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The domain restriction is that x cannot equal 1, as it would make the denominator zero.

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none

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

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What is the process to solve a radical equation?

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To solve a radical equation, isolate the radical on one side and then square both sides to eliminate the radical.