Voltage Division Rule:

 Since in series circuit, shown in Figure, current is illustrated by equation

I =  V /R_eq

then

 V₁ = IR₁ = V.  (R₁/R_eq)

V₂ = IR₂ = V.  (R₂ /R_eq)

V₃ = IR₃ = V.  (R₃ /R_eq)

Figure shows the resistance connected is parallel.

Figure: Parallel Resistors

In parallel circuits, current is divided whereas the voltage remains same across all parallel branches.

1 /R_eq =  (1 / R₁ )+  (1 / R₂) +  (1/ R₃)

= (R₂ R₃  + R₁ R₃  + R₁ R₂ )/ R₁ R₂ R₃

∴          R_eq = R₁ R₂ R₃ / (R₁ R₂ + R₂ R₃ + R₃ R₁)

It is better to represent the circuit in conductance form.

i.e. G_eq  = G₁ + G₂ + G₃