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The graph of y = (5x^2 - 9)/(3x^2 + 6x + 2) has vertical asymptotes at x = a and x = b.  Find a + b.

 Nov 30, 2020
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Okay, so the two asymptotes are -(3+√3)/3 & -(3-√3)/3

So, add both asymptotes.

 

\(-\frac{3+\sqrt{3}}{3}+\frac{3-\sqrt{3}}{3}\)\(=\frac{-\left(3+\sqrt{3}\right)+3-\sqrt{3}}{3}\)

Expand:

\(=\frac{-2\sqrt{3}}{3}\) \(=-\frac{2\sqrt{3}}{3}\)

 

The answer is \(=-\frac{2\sqrt{3}}{3} \)

Here is the graph:

 Nov 30, 2020

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