Complex Rational Expressions

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Define a complex rational expression.

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What is the first step in simplifying a complex rational expression?

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The first step is to find a common denominator for the fractions in the numerator and the denominator.

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What is the formula for finding a common denominator?

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The common denominator is the least common multiple (LCM) of the denominators involved in the fractions.

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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 simplest form, removing any common factors in the numerator and denominator.

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What is the significance of factoring in simplifying rational expressions?

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Factoring helps to identify and cancel out common factors in the numerator and denominator, simplifying the expression.

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What is the relationship between complex rational expressions and polynomial long division?

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Complex rational expressions can sometimes be simplified using polynomial long division when the degree of the numerator is greater than or equal to the degree of the denominator.