I was calculating the parallel resistance for a circuit, but just couldn't get the correct answer despite several attempts. I felt incredibly dumb when I watched a video on how to calculate parallel resistance and realized I forgot to take the final inverse after summing all the terms:

For example, suppose we have a parallel circuit with resistors of
30 Ohms, 60 Ohms, 20 Ohms and 10 Ohms. Then the total resistance 

$$\frac{1}{R\_t} = \frac{1}{30} + \frac{1}{60} + \frac{1}{20} + \frac{1}{10} = \frac{2}{60} + \frac{1}{60} + \frac{3}{60} + \frac{6}{60} = \frac{12}{60} = \frac{1}{5}$$
$$R\_t = 5 $$

I realized my answer was 1/Rt, not Rt. I kept forgetting to take the final inverse! I became furious when I recalled this wasn't the first time I made this mistake. The video lecturer said it was a very common error.

Why do electronics textbooks and teaching materials use this error prone formula instead of the simplified (variable isolated?) form:

$$ R\_t = \frac{1}{\frac{1}{R\_1} + \frac{1}{R\_2} +\frac{1}{R\_3} ...} $$

You rarely see other formulas expressed as a non-isolated variable in an equation. Consequently, it's very easy to overlook the final inverse operation. Why is this form so commonly presented? I suspect it is used for pedagogical reasons to help students understand the underlying concepts, but unsure.