Rationals Assignment

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What is the definition of the Least Common Denominator (LCD)?

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The Least Common Denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.

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How do you find the LCD of the fractions 5/4 and 2/3?

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To find the LCD of 5/4 and 2/3, identify the least common multiple of the denominators 4 and 3, which is 12.

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What is the LCD of the expressions x^2(x - 2) and x(x - 2)?

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The LCD is x(x - 2).

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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 check for extraneous solutions?

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To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

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What is the significance of factoring in finding the LCD?

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Factoring helps to identify the unique factors in the denominators, which is essential for determining the LCD.

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What is the process of solving rational equations?

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The process includes finding the LCD, rewriting each fraction with the LCD, eliminating the denominators, and solving the resulting equation.