We have
[tex]f(x)=\frac{2x^2+x}{x^2-5x+6}[/tex]
First we will factorize the function
[tex]f(x)=\frac{x(2x+1)}{\mleft(x-2\mright)(x-3)}[/tex]
The domain is
[tex]\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)[/tex]
In this case, we have two vertical asymptotes
x-2=0
x=2
x-3=0
x=3
ANSWER
The domain is
[tex]\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)[/tex]
The vertical asymtotes
x-2=0
x=2
x-3=0
x=3
