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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.

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  • $\begingroup$ sometimes a “dumb questions” can be instructive $\endgroup$ – user28715 Mar 2 '19 at 0:54
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$$2s+1=2\left(s+\frac12\right)$$ That's all I can say.

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  • $\begingroup$ Oops, I think I’ll delete the question. $\endgroup$ – rhody Mar 1 '19 at 19:05
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Anyone with a brain will realize I made an extremely elementary arithmetic error in my question. The transformed equation should of course be:

enter image description here

which means the zero is -1/2 as expected. The bottom line is that a gain has no effect on the values of the zeros since it is just a scaling factor in the zero polynomial.

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