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The graph of \(y=\frac{5x^2-9}{3x^2+5x+2}\) has vertical asymptotes at \(x = a\) and \(x = b\). Find \(a + b.\)

 

The formula for the vertical asymptote of a equation of the form \(ax + b/cx + d\) is \(x = -d/c\). For the horizontal asymptote, the formula is \(x = a/c\).

The denominator of the fraction can be expanded into \((3x + 2)(x + 1)\). I don't know what to do next. 

 Jun 13, 2018
 #1
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You basically have it, all you have to do is set the denominator equal to 0 and isolate the x. 
3x+2=0 --> x=-2/3
x+1=0 --> x=-1
There's your a and b.
Add them.
-1+(-2/3)=-5/3

 Jun 13, 2018

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