Simplifying Rational Expressions and LCD

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What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

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What is the domain of a rational function?

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The domain of a rational function is the set of all real numbers except where the denominator is zero.

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How do you find the domain of the function f(x) = x / (x^2 - 25)?

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Set the denominator x^2 - 25 = 0. Solve for x to find x = 5 and x = -5. The domain is (-∞, -5) U (-5, 5) U (5, ∞).

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What is the least common denominator (LCD)?

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The least common denominator (LCD) is the smallest expression that can be used as a common denominator for two or more fractions.

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What is the domain of the function f(x) = 3/(x + 2)?

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The domain is all real numbers except x = -2, so it is (-∞, -2) U (-2, ∞).

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What happens to the domain of a function when the denominator is zero?

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When the denominator is zero, the function is undefined at that point, and it is excluded from the domain.

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How do you solve the equation 2x + 3 = 9 for x?

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Subtract 3 from both sides to get 2x = 6, then divide by 2 to find x = 3.

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