### Instruction: The graph of $y=\frac{5x^2-9}{3x^2+5x+2}$ has vertical asymptotes at $x = a$ and $x = b$.  Find $a + b$.### Response: To find the vertical asymptotes of a rational function, I need to factor the denominator and set it equal to zero.
I can use the quadratic formula to find the roots of $3x^2+5x+2=0$.
The formula is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, where $a=3$, $b=5$, and $c=2$.
Plugging these values into the formula, I get $x=\frac{-5\pm\sqrt{25-24}}{6}$.
Simplifying, I get $x=\frac{-5\pm 1}{6}$.
So the roots are $x=\frac{-5+1}{6}=-\frac{2}{3}$ and $x=\frac{-5-1}{6}=-1$.
These are the values of $a$ and $b$, so $a+b=-\frac{2}{3}-1=-\frac{5}{3}$.