# What is the zero in this transfer function?

What is the zero for the following transfer function, $$-1/2$$ or $$-2$$?

$$H(s) = \frac{2s +1}{(s + 3)(s + 2)}$$

This appears to give a zero of $$-1/2$$.

I can transform this into the standard form that includes the gain $$K$$:

$$H(s) = \frac 12 \left(\frac{s + 2}{(s + 3)(s + 2)}\right)$$

Where the leading half is the gain. The zero now appears to be $$-2$$. What is the conceptual error I am making? Should I take the gain out or leave it in the numerator?

UPDATE: I think this question is worthy of deletion given the nature of the error but I am unable to. Instead, see my answer below.

• sometimes a “dumb questions” can be instructive – user28715 Mar 2 '19 at 0:54

$$2s+1=2\left(s+\frac12\right)$$ That's all I can say.