Rational Equations

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What is a rational equation?
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A rational equation is an equation that contains one or more rational expressions.
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How do you solve a rational equation?
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To solve a rational equation, find a common denominator, eliminate the fractions, then solve the resulting equation.
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What must you check for after solving a rational equation?
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Check for extraneous solutions because multiplying by the common denominator may introduce false solutions.
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What is a rational expression?
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A rational expression is a ratio of two polynomials.
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Give an example of a simple rational equation.
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An example is (x/2) + (3/x) = 1.
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How can rational equations be useful?
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Rational equations are used in real-life problems involving rates, such as speed, work, or fluid flow.
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What is extraneous solution?
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An extraneous solution is a solution derived from an equation that is not valid for the original equation.
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What precautions should you take when solving rational equations?
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Avoid solutions that make any denominator zero.
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Why is finding a common denominator important in solving rational equations?
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It allows you to eliminate fractions to simplify the equation.
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What happens if you divide by zero in a rational equation?
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Dividing by zero is undefined, so it makes the equation invalid.
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What do you do if different denominators appear in a rational equation?
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Multiply each term by the least common denominator to eliminate the fractions.
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How is solving x/(x-1) = 2 done?
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Multiply each side by (x-1), then solve: x = 2(x-1).
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What should you do if your solution makes a denominator zero?
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Discard that solution as it is extraneous.
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Explain the term 'least common denominator' in context of rational equations.
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It is the smallest expression that all denominators in the equation can divide into without a remainder.
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What is a polynomial?
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A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
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