Simplify Rational Expressions

How to simplify rational expressions? A tutorial with examples and detailled solutions is presented.

To simplify a rational expression, we first factor both the numerator and denominator completely then reduce the expression by cancelling common factors.

Example 1: Simplify the rational expression

rational expressions 1

Detailed Solution to Example 1

  • Factor both the numerator and denominator completely.
    rational expressions 2

  • Cancel common factors to reduce and simplify the given expression.
    rational expressions 3

    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

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Detailed Solution to Example 2

  • Factor both the numerator and denominator completely.
    rational expressions 5

  • Cancel common factors to simplify the expression.
    rational expressions 6




Example 3: Simplify the rational expression

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Detailed Solution to Example 3

  • Factor both the numerator and denominator completely.
    rational expressions 8

  • Note that - x + 1 = - (x - 1) in the denominator.
    rational expressions 9

  • Cancel common factors.
    rational expressions 10

Exercises

Simplify the rational expression.

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Answers to the above exercises



More references to topics related to rational expressions.


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    Updated: February 2015

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