Simplify, Multiply & Divide Rational Expressions

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What is a rational expression?

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

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How do you simplify a rational expression?

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To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

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What is the process for multiplying rational expressions?

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To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

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What is the process for dividing rational expressions?

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To divide rational expressions, multiply by the reciprocal of the divisor and then simplify.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

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What is the difference between a proper and improper rational expression?

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A proper rational expression has a degree of the numerator less than the degree of the denominator, while an improper one has a degree of the numerator greater than or equal to the degree of the denominator.

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How do you find the least common denominator (LCD) of rational expressions?

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The LCD is found by determining the least common multiple of the denominators of the rational expressions.

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What is the significance of excluding values in rational expressions?

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Excluding values is important because they make the denominator zero, which is undefined in mathematics.

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