SOLUTION: Identify all asymptotes and holes in the graph of each rational function: f(x)= 3x^2+x-4/x^2+2x-3 please help if you can! all i know how to do is to factor the denominator

Question 79289: Identify all asymptotes and holes in the graph of each rational function:
f(x)= 3x^2+x-4/x^2+2x-3
please help if you can! all i know how to do is to factor the denominator
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Identify all asymptotes and holes in the graph of each rational function:
f(x)= 3x^2+x-4/x^2+2x-3
f(x)=[3x^2+4x-3x-4]/[(x+3)(x-1)]
f(x)=[x(3x+4)-(3x+4)]/[(x+3)(x-1)]
f(x)=[(3x+4)(x-1)]/[(x+3)(x-1)]
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Since there is an (x-1) factor in the numerator and denominator
f(x) has a hole at x=1.
There is a vertical asymptote at x=-1.
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Cheers,
Stan H.
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