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# asymptotes

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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

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

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