Answer:
x = -9 and x = -10
Step-by-step explanation:
[tex]f(x)=\dfrac{x^2+11x+18}{x^2+19x+90}\\\\\text{DOMAIN:}\\\\x^2+19x+90\neq0\\\\x^2+9x+10x+90\neq0\\\\x(x+9)+10(x+9)\neq0\\\\(x+9)(x+10)\neq0\iff x+9\neq0\ \wedge\ x+10\neq0\\\\x\neq-9\ \wedge\ x\neq-10[/tex]
[tex]\\\\\text{Therefore the vertical asymptotes are:}\\\\x=-9\ and\ x=-10.[/tex]
