SOLUTION: I am so lost, if anyone could please answer this one I'd really appreciate it: {{{What is the domain of g(x) when g(x)=(x+3)/(2x-5)}}

Question 93238: I am so lost, if anyone could please answer this one I'd really appreciate it: What is the domain of g(x) when g(x)=(x+3)/(2x-5)}}
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
In domain problems you are looking for values of x ... in particular you are looking for
any values that x cannot have.
.
In this problem you are given:
.

.
Notice that you are dividing by . Recall that division by zero is not allowed
in algebra. So the denominator cannot be zero. This means that:
.

.
is not allowed to happen. So solve this equation to find out what value of x would make
the denominator equal to zero.
.
Begin by adding +5 to both sides of the equation to get rid of the -5 on the left side.
This addition to both sides makes the equation become:
.

.
Then solve for x by dividing both sides of the equation by 2 to get:
.

.
This says that x cannot have the value because if it does, the denominator
of the given expression becomes zero and, as you know, division by zero is not permitted.
.
Other than that there is no other value of x that causes a problem. Since the domain is
the values that x is allowed to have you can say that x can be any value from minus infinity
to plus infinity except x cannot be .
.
Hope this helps you to understand the problem. In domain problems one of the things
to always look for is "are there any terms that will cause a division by zero?" and solve
those terms for values of x that will cause them to go to zero. Those are values that x
cannot be allowed to take.
.
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