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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

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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