SOLUTION: What's the domain of f(x)=x/(x^2+2x-3

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Question 549306: What's the domain of f(x)=x/(x^2+2x-3
Found 2 solutions by mathie123, stanbon:
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%2F%28x%5E2%2B2x-3%29



Note that the numerator can be any value of x.... but whenever we are dealing with fractions, the denominator cannot be 0 (check out any number divided by 0 on your calculator if you do not believe me.... you will end up getting an error)
This means that
x%5E2%2B2x-3 cannot be 0
Well when does x%5E2%2B2x-3=0??
x%5E2%2B2x-3
Since our a value is 1, we need two values that multiply to our c value (-3) and add to our b value (2). If you think about it you will see that 3 and -1 do the trick.
So
x%5E2%2B2x-3=%28x%2B3%29%28x-1%29
and
%28x%2B3%29%28x-1%29=0 when x=-3 and x=1
This means x can be anything except -3 and 1.

Let me know if any of the steps I took you are not sure about:) Merry Christmas!

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What's the domain of f(x)=x/(x^2+2x-3)
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That denominator cannot be zero:
x^2+2x-3 = 0
(x+3)(x-1) = 0
x = -3 ; x = 1
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Domain is "All Real Numbers except x = -3 and x = 1.
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Cheers,
Stan H.