Solving rational expressions

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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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How do you solve a rational expression?

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To solve a rational expression, find a common denominator, combine the fractions, and then solve for the variable.

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What are extraneous solutions?

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Extraneous solutions are solutions that emerge from the algebraic process but do not satisfy the original equation.

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How can you check for extraneous solutions?

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Substitute the solution back into the original equation to see if it holds true.

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What is the first step in solving a rational equation?

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The first step is to identify and exclude any values that make the denominator zero.

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What does it mean to simplify a rational expression?

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Simplifying a rational expression means reducing it to its lowest terms by factoring and canceling common factors.

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What is the importance of finding a common denominator?

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Finding a common denominator allows you to combine multiple rational expressions into a single expression.

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What is the process of factoring in rational expressions?

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Factoring involves rewriting a polynomial as a product of its factors to simplify the expression.

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What is the difference between a rational expression and a rational number?

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A rational expression is a fraction of polynomials, while a rational number is a fraction of integers.

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How do you identify restrictions in rational expressions?

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Restrictions are identified by setting the denominator equal to zero and solving for the variable.