Fractions swapped

Question

I am following an electronics tutorial (slide 23 here) and at some point, he shows the formula:

$\frac{Vs}{Ri} + \frac{Vo}{Rf} = 0$

Vs, Ri, Vo and Rf are just variables for voltage and resistance. After some rearanging, it becomes:

$\frac{Vo}{Vs} = - \frac{Rf}{Ri}$

How did the fractions "swap"?

Answer 1

$$\frac{Vs}{Ri} + \frac{Vo}{Rf} = 0$$ $$ \frac{Vo}{Rf} = -\frac{Vs}{Ri} $$ $$ \frac{Vo \times Ri}{Rf} = -Vs $$ $$ Vo\times Ri = -Vs\times Rf $$ $$ \frac{Vo\times Ri}{Vs} = -Rf $$ $$ \frac{Vo}{Vs} = -\frac{Rf}{Ri} $$

Answer 2

$$\frac{V_s}{R_i}+\frac{V_o}{R_f}=0 \Leftrightarrow \frac{V_o}{R_f} =-\frac{V_s}{R_i} $$

Now multiplying each side by $\frac{R_f}{V_s}$ yields $$\frac{V_o}{V_s}=-\frac{R_f}{R_i}$$