gjhfdfg
Find the vertical asymptotes, if any, of the graph of the rational function.



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gjhfdfg
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f(x)= \[\frac{ x }{ x^2 +1 }\]

jim_thompson5910
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solve
x^2 + 1 = 0
for x

jim_thompson5910
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tell me what you get

gjhfdfg
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Would it just be x^2 = 1 ?

jim_thompson5910
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good so far, what's next?

k.rajabhishek
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there will be no vertical asymptote

gjhfdfg
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Hmm, Im not sure? Do I replace the variable with 1?

jim_thompson5910
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take the square root of both sides
x = sqrt(1) or x = sqrt(1)
but there's a problem, you can't take the square root of 1 and get a real number

jim_thompson5910
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so x^2 + 1 = 0 has no real solutions

jim_thompson5910
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leading to the fact that \[\Large \frac{ x }{ x^2 +1 }\] has no vertical asymptotes

gjhfdfg
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Ah, ok. Thank you.!
Just out of curiosity, what happened to the x on top of the fraction?

jim_thompson5910
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the numerator doesn't play any role in finding the vertical asymptotes unless you can make it cancel with something in the denominator

jim_thompson5910
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if you had something like
x

x^2+x
the fraction would simplify to
1
________
x + 1
and this would be a case where the numerator plays a role

gjhfdfg
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So basically the numerator was pointless in this equation?

jim_thompson5910
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pretty much

jim_thompson5910
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the basic thing is to simplify as much as possible (which couldn't be done in this case)
then look at the denominator only

gjhfdfg
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Got it, thank you again.!

jim_thompson5910
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sure thing