a,b, and c are nonzero constants, all different. x = - c is a vertical asymptote.?

Question

I set up a problem as:

a=1

b=2

c=3

f(x)=((x-1)(x-2)(x+3))/((x+2)(x+3))

I found a vertical asymptotes at x= -2

So this is false correct?

Because -c is -3 not -2

Update:

so I am wrong? It is true?

Answer 1

f(x) = (x-a)(x-b)(x+c)/{(x+b)(x-+)}

Set x = -c --> f(-c) --> infinity and df/dx|x = -c --> infinity

THerefore x = -c is a vertical asymptote