Defining the Domain

Any fraction that contains a variable in the denominator has the possibility of being undefined for some value of the variable.  Remember, a “variable” means that the value for the letter may “vary.”  Any value which would make the denominator equal to zero must be eliminated as a possibility for the variable.  To find such a value, we set the denominator equal to zero and solve.
For example in the fraction     x – 2  is in the denominator.  If we set x – 2 = 0 and solve we find that x cannot equal 2 since the value of 2 for the variable x would cause the denominator to equal zero.  Fractions are said to be “undefined” when the denominator equals zero.
For the fraction    you would have to first factor the denominator and then set those factors containing a variable equal to zero and find the replacement values for the variable.
 

  so x cannot equal -3 or x cannot equal 3, since these values would create a zero in the denominator.

General Algebra Tips

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This page was edited on 19-Sep-2007