WEBVTT

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Here is the problem: (x cubed minus 1)/(x minus 1).

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Simplify the rational expression in x: factor, cancel common factors and state excluded values.

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Write as a single fraction.

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Factor the numerator and denominator.

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Cancel the common factor. The factor x minus 1 appears in both the numerator and the denominator. Cancelling it does not change the value wherever the original expression is defined.

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State the excluded values. The original expression is undefined where any denominator (or divisor) is zero: x not equal to 1. These restrictions stay even if a factor cancelled.

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So the answer is x squared plus x plus 1, for x not equal to 1.

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In lowest terms the result is x squared plus x plus 1. Excluded values: x not equal to 1.

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The simplified form was compared with the original at four test points and agrees.