# Deriving simple voltage equation

$$V_o = \frac{V_s \cdot R_2}{R_1 \cdot (1+R_2/R_L)+R_2}$$

I need to derive this equation given this circuit:

This is what I have so far.

$$I=\dfrac{V_s}{R_1+\dfrac{R_2 \cdot R_L}{R_2+R_L}}$$

$$V_{R_L} = I \cdot R_L$$

Where am I going wrong?

If R$_L$ wasn't present the voltage output would just be: -

$V_{S}\times\dfrac{R_2}{R_1 + R_2}$

So, adjust R2 mathematically to account for R$_L$ being in parallel with it.

Can you take it from here?

Your equation for $I$ is correct. The next step is

$$V_o = I \cdot (R_2||R_L)$$

$$I = \dfrac{V_s}{R_1+\dfrac{R_2 \cdot R_L}{R_2+R_L}}$$ is correct.

$V_{R_L} = I \cdot R_L$ is the wrong part.

$$V_{R_L} = I \cdot R_{\text{eq}}; R_{\text{eq}} = R_L|| R_2 = \dfrac{R_LR_2}{R_L+R_2}$$