Question 93239
What is the domain of g(x) when:
{{{g(x) = (x+3)/(2x-5)}}} 
You'll recall, no doubt, that the domain of a function is the set of all possible values of the independent variable, which is x in this case.
First, we need to examine the denominator of the given function (2x-5) and ask..."what value of x will cause this to become zero?"
You can find out by setting the denominator equal to zero and solving for x.
{{{2x-5 = 0}}} Add 5 to both sides.
{{{2x = 5}}} Divide both sides by 2.
{{{x = 5/2}}}
So, when {{{x = 5/2}}} the denominator of the function becomes zero, and, as you know, mathematics does not allow division by zero.  It undefined. Therefore, we must exclude {{{x = 5/2}}} from the domain.  All other real values of x, however, are legal, so we can write the domain as:
{{{(5/2)>x>(5/2)}}}
You would read this as..."all the real numbers not incuding 5/2"