Simplify 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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What does it mean to simplify a rational expression?

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To simplify a rational expression means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

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The first step is to check if there are any common factors in the numerator and the denominator.

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No, the expression cannot be simplified further because there are no common factors.

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The variable x cannot be equal to 1 or 3, as these values would make the denominator zero.

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What is the definition of a polynomial?

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A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.

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The degree of the polynomial in the numerator, which is (x+2), is 1.

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The degree of the polynomial in the denominator, which is (x-1)(x-3), is 2.

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What does it mean for a rational expression to be in simplest form?

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A rational expression is in simplest form when the numerator and denominator have no common factors other than 1.

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What is a common factor?

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A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.