Equation transposition

Question

I am struggling to see how an equation has been transposed. It is probably pretty easy, so apologies in advance.

If possible; please show the transposition stages:

$V_{out} = V1 . \frac{R2}{R1 + R2} (\frac{R3 + R4}{R3}) - V2 . \frac {R4} {R3}$

this is then transposed to.....

$V_{out} = (V1 - V2) \frac {R4} {R3}$

Answer 1

Without further conditions relating $R_1, R_2, R_3, R_4$ to one another, these two equations are not equivalent.

EDIT: You say that $R_1 = R_3$ and $R_2 = R_4$. In that case,

\begin{align*} V_1 &\left(\frac{R_2}{R_1 + R_2}\right) \left(\frac{R_3 + R_4}{R_3}\right) - V_2 . \frac {R_4} {R_3} \\[3mm] &= V_1 \left(\frac{R_4}{R_3 + R_4}\right) \left(\frac{R_3 + R_4}{R_3}\right) - V_2 \frac {R_4} {R_3} \\[3mm] &= V1 \frac{R_4}{R_3} - V2 \frac {R_4} {R_3} = (V1 - V2) \frac{R_4}{R_3} \end{align*}