
Detailed Solution to Example 1
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Factor both the numerator and denominator completely.

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Cancel common factors to reduce and simplify the given expression.

Note: The given expression is equal to 2 on the condition that x is not equal to 1. x = 1 is not in the domain of the expression.
Example 2: Simplify the rational expression

Detailed Solution to Example 2
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Factor both the numerator and denominator completely.

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Cancel common factors to simplify the expression.
Example 3: Simplify the rational expression

Detailed Solution to Example 3
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Factor both the numerator and denominator completely.

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Note that - x + 1 = - (x - 1) in the denominator.

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Cancel common factors.
Exercises
Simplify the rational expression.
Answers to the above exercises
More references to topics related to rational expressions.