Question 90539
Set the denominator equal to zero (remember: dividing by zero is not allowed)


{{{x^2-14x+49=0}}}


{{{(x-7)(x-7)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:


{{{x-7=0}}} or {{{x-7=0}}} 


{{{x=7}}} or {{{x=7}}}   Now solve for x in each case


Since these two answers are the same, our only answer is {{{x=7}}}


Since {{{x=7}}} makes the entire denominator equal to zero, this means {{{x=7}}} is excluded from the domain.



Notice if we graph {{{x^2/(x^2-14x+49)}}} we get


{{{ graph( 500, 500, -5, 15, -5, 15, x^2/(x^2-14x+49)) }}}


and we can see that there is a discontinuity at {{{x=7}}}, so this verifies our answer.