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How to Simplify Rational expressions

Reduce & Simplify

Simplifying rational expressions requires good factoring skills. The twist now is that you are looking for factors that are common to both the numerator and the denominator of the rational expression.
  • 1) Look for factors that are common to the numerator & denominator
  • 2) 3x is a common factor the numerator & denominator. Note that it is clear that x ≠0
  • 3) Cancel the common factor
  • 4) If possible, look for other factors that are common to the numerator and denominator. In our example, we can use foil in reverse to factor an (x − 1) in the denominator and further cancel this binomial from both the numerator and the denominator.
  • 5) After cancelling, you are left with 1/(x-1)


  • 6) The final simplified rational expression is valid for all values of x except 0 and 1.