Solving Rational Equations

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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 is a polynomial.

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How do you solve a rational equation?

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To solve a rational equation, you can find a common denominator, eliminate the fractions, and then solve the resulting polynomial equation.

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What is cross-multiplication in rational equations?

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Cross-multiplication is a method used to solve equations of the form a/b = c/d by multiplying the numerator of one fraction by the denominator of the other.

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What does it mean if a rational equation has no solution?

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A rational equation has no solution if the equation leads to a contradiction, such as an impossible statement like 0 = 5.

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What is the first step in solving the equation 1/(x-2) = 3/4?

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The first step is to cross-multiply to eliminate the fractions: 1 * 4 = 3 * (x - 2).

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How do you check your solution in a rational equation?

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To check your solution, substitute the value back into the original equation to see if both sides are equal.

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What is a common mistake when solving rational equations?

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A common mistake is failing to check for extraneous solutions, which are values that do not satisfy the original equation.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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How do you find the least common denominator (LCD) in rational equations?

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The least common denominator is found by identifying the least common multiple of the denominators involved in the rational expressions.

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What is the significance of factoring in solving rational equations?

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Factoring can simplify the equation and make it easier to find solutions by setting each factor equal to zero.