Test Rational Expressions/Equations

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What is a rational expression?

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A rational expression is a fraction where the numerator and the denominator are both polynomials.

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What does it mean to simplify a rational expression?

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To simplify a rational expression means to reduce it to its lowest terms by factoring and canceling common factors.

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What is cross-multiplication?

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Cross-multiplication is a method used to solve equations involving two fractions by multiplying the numerator of one fraction by the denominator of the other.

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x = 4 + 2 = 6.

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What is the first step in solving a rational equation?

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The first step is to identify any restrictions on the variable that would make the denominator zero.

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How do you find the least common denominator (LCD) of rational expressions?

Back

The LCD is found by determining the least common multiple of the denominators of the rational expressions.

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What does it mean if a rational equation has no solution?

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It means that the equation leads to a contradiction, such as a statement that is always false.

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x = 2.

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What is the importance of checking for extraneous solutions?

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Checking for extraneous solutions ensures that the solutions found do not make any denominator zero in the original equation.