Question 867044
You cannot divide by zero. So {{{x^2 - 49}}} cannot be zero. 



If it were, then 



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



{{{(x-7)(x+7) = 0}}}



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



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



These two values cause the denominator to be zero. 



So they must be kicked out of the domain to make sure the entire rational expression is defined.



Therefore, the domain is the set of all real numbers BUT x cannot equal -7 and x cannot equal 7. The value of x can be any other number.



In interval notation, the domain is <img src="http://www.sciweavers.org/tex2img.php?eq=%5Cleft%28-%5Cinfty%2C-7%5Cright%29%5Ccup%5Cleft%28-7%2C7%5Cright%29%5Ccup%5Cleft%287%2C%5Cinfty%5Cright%29&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="\left(-\infty,-7\right)\cup\left(-7,7\right)\cup\left(7,\infty\right)" width="225" height="18" />