Solving Rational Equations and inequalities

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What is a rational equation?

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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.

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How do you solve a rational equation?

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To solve a rational equation, first find a common denominator, eliminate the fractions by multiplying both sides by this denominator, and then solve the resulting polynomial equation.

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What is the importance of checking for extraneous solutions in rational equations?

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Checking for extraneous solutions is important because multiplying both sides of an equation by a variable expression can introduce solutions that do not satisfy the original equation.

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What is a rational inequality?

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How do you solve a rational inequality?

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To solve a rational inequality, first find the critical points by setting the numerator and denominator to zero, then test intervals between these points to determine where the inequality holds true.

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What is a critical point in the context of rational equations?

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A critical point is a value of the variable that makes the numerator or denominator of a rational expression equal to zero, which can affect the solution of the equation or inequality.

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What does it mean for a rational expression to be undefined?

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A rational expression is undefined when its denominator equals zero, as division by zero is not possible.

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What is the process of finding the least common denominator (LCD) in rational equations?

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The least common denominator (LCD) is found by determining the least common multiple of the denominators of all rational expressions involved.