Solving Rational Equations (Proportions)

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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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What does it mean to solve a proportion?

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To solve a proportion means to find the value of the variable that makes the two ratios equal.

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What is cross-multiplication?

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Cross-multiplication is a method used to solve proportions by multiplying the numerator of one fraction by the denominator of the other fraction.

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Cross-multiply to get: 5(x + 1) = 20. Then, solve for x to find x = 3.

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Cross-multiply to get: 4 * 10 = 8 * x. Thus, x = 5.

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What is the first step in solving a rational equation?

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The first step is to eliminate the fractions by finding a common denominator or cross-multiplying.

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

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It means that there is no value for the variable that can satisfy the equation, often due to a contradiction.

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What is the importance of checking your solution in rational equations?

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Checking your solution is important to ensure that it does not make any denominator zero, which would make the equation undefined.

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Cross-multiply to get: 5(x - 2) = 12. Then, solve for x to find x = 4.4.

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What is a common mistake when solving rational equations?

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A common mistake is forgetting to check for extraneous solutions that may arise from the process of solving.