Rational Equations Flashcard

Front

What is 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/or denominator are polynomials.

Front

What is the first step in solving a rational equation?

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The first step is to identify the common denominator and multiply all terms by it to eliminate the fractions.

Front

Why is it important to check for excluded values when solving rational equations?

Back

Excluded values are values that make the denominator zero, which would make the expression undefined. Checking for these values ensures the solution is valid.

Front

What does it mean to cross multiply in a rational equation?

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Cross multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction, allowing the equation to be rewritten without fractions.

Front

How do you find the critical points in a rational inequality?

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Critical points are found by setting the numerator and denominator equal to zero and solving for x. These points help determine the intervals to test for the inequality.

Front

What is the significance of combining terms in a rational inequality?

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Combining terms into a single rational expression simplifies the inequality, making it easier to analyze and solve.

Front

What is the process for solving a rational inequality?

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1. Rewrite the inequality to have a zero on one side. 2. Combine into a single rational expression. 3. Identify critical points. 4. Test intervals to determine where the inequality holds.

Front

What is a common mistake when solving rational equations?

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A common mistake is to ignore the excluded values, which can lead to invalid solutions.

Front

What does it mean to simplify a rational expression?

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Simplifying a rational expression involves reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Front

How do you determine the domain of a rational function?

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The domain of a rational function includes all real numbers except those that make the denominator zero.