Voltage divider formula?

Actually I am not able to understand how the author arrived at this equation using voltage divider formula ?

what I tried is , I combined the two 2R resistor connected to ground in series and wrote 4R then, it is in parallel with the single R resistor .

I am confused where I made the mistake, and also I request you to please provide any general rule for this method .

• The 2R resistors are not in series with each other. Commented Mar 24, 2022 at 14:09

Here's a hint. Using Thevenin's theorem, you can simplify the circuit like this: -

It should be a walk in the park for the next step.

Here is my method, which I think is valid.

First, let's label the resistors:

Then redraw the circuit so that it's easier to see what's going on:

simulate this circuit – Schematic created using CircuitLab

Now, find the voltage at node A. From there it's easy to find Vin.

If you just want to use the voltage divider formula you can first calculate the voltage at the junction point which is:

Vx = $$\ \frac{+V\cdot (3 || 2)}{3||2 + 2} \$$ = $$\+V\cdot\frac{3}{8}\$$

Then apply the divider formula again to get Vin

2/3 * 3/8 = 1/4