Lois C. answered • 04/21/20
BA in secondary math ed with 20+ years of classroom experience
The only way that a rational expression will be undefined is if the denominator has a value of 0. If the denominator contains variables, as this one does, we need to determine what values of the variable(s) will make the denominator = 0.
With this problem, we begin by writing the denominator in factored form. This will make it easier for us to determine which values of x will make the denominator = 0. Since the terms in the denominator have a GCF ( i.e. Greatest Common Factor) of x, we factor it out and get x(x-7) in the denominator. Using the Zero Product Property, we know that for the denominator to = 0, either one factor or the other factor in the denominator must = 0. So either x = 0 or x - 7 = 0. Solving the second equation for x, we get x = 7. So these two values, x = 0 and x = 7, are the values that make the denominator = 0 and are thus the two values for x that make the expression undefined.
