Question 878939
You cannot divide by zero. If the denominator were zero, then 


2x-6 = 0


2x = 6


x = 6/2


x = 3


That means if x = 3, then the denominator 2x-6 would be equal to zero.


So x = 3 causes a division by zero error. That forces us to exclude x = 3 from the domain.


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Domain: the set of all real numbers x but x cannot equal 3


Another way to state the domain


<img src="http://www.sciweavers.org/tex2img.php?eq=%5Ctext%7BDomain%3A%20%7D%5Cleft%5C%7Bx%7Cx%5Cin%5Cmathbb%7BR%7D%2Cx%20%5Cneq%203%5Cright%5C%7D&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="\text{Domain: }\left\{x|x\in\mathbb{R},x \neq 3\right\}" width="268" height="18" />


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Domain in interval notation:


<img src="http://www.sciweavers.org/tex2img.php?eq=%5Cleft%28-%5Cinfty%2C3%5Cright%29%20%5Ccup%20%5Cleft%283%2C%5Cinfty%5Cright%29&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="\left(-\infty,3\right) \cup \left(3,\infty\right)" width="136" height="18" />