WEBVTT

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Here is the problem: 1/(x minus 1) minus 1/(x plus 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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No common factors remain. The numerator and denominator share no polynomial factor, so the fraction is already in lowest terms.

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

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So the answer is 2/((x minus 1)(x plus 1)), for x not equal to negative 1, x not equal to 1.

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In lowest terms the result is 2/((x minus 1)(x plus 1)) (expanded: 2/(x squared minus 1)). Excluded values: x not equal to negative 1, x not equal to 1.

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