Question 93238
In domain problems you are looking for values of x ... in particular you are looking for
any values that x cannot have.
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In this problem you are given:
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{{{g(x)=(x+3)/(2x-5)}}}
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Notice that you are dividing by {{{(2x - 5)}}}.  Recall that division by zero is not allowed
in algebra.  So the denominator cannot be zero. This means that:
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{{{2x - 5 = 0}}}
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is not allowed to happen. So solve this equation to find out what value of x would make 
the denominator equal to zero.
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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:
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{{{2x = 5}}}
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Then solve for x by dividing both sides of the equation by 2 to get:
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{{{x = 5/2}}}
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This says that x cannot have the value {{{5/2}}} because if it does, the denominator
of the given expression becomes zero and, as you know, division by zero is not permitted.
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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 {{{5/2}}}. 
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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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