Change variable $$I$$ to $$I_1$$ and $$R$$ to $$R_1$$ in Eq. \ref{eq:8922008}; yields Eq. \ref{eq:8148802}. \begin{equation} V = I_1 R_1 \label{eq:8148802} \end{equation} Change variable $$I$$ to $$I_2$$ and $$R$$ to $$R_2$$ in Eq. \ref{eq:8922008}; yields Eq. \ref{eq:6313158}. \begin{equation} V = I_2 R_2 \label{eq:6313158} \end{equation} Divide both sides of Eq. \ref{eq:6313158} by $$R_2$$; yields Eq. \ref{eq:4037937}. \begin{equation} \frac{V}{R_2} = I_2 \label{eq:4037937} \end{equation} Divide both sides of Eq. \ref{eq:8148802} by $$R_1$$; yields Eq. \ref{eq:5168370}. \begin{equation} \frac{V}{R_1} = I_1 \label{eq:5168370} \end{equation} Eq. \ref{eq:3843569} is an initial equation. current flows through both resistors \begin{equation} I_{\rm total} = I_1 + I_2 \label{eq:3843569} \end{equation} Change variable $$I$$ to $$I_{\rm total}$$ and $$R$$ to $$R_{\rm total}$$ in Eq. \ref{eq:8922008}; yields Eq. \ref{eq:8002723}. \begin{equation} V = I_{\rm total} R_{\rm total} \label{eq:8002723} \end{equation} Divide both sides of Eq. \ref{eq:8002723} by $$R_{\rm total}$$; yields Eq. \ref{eq:1708642}. \begin{equation} \frac{V}{R_{\rm total}} = I_{\rm total} \label{eq:1708642} \end{equation} Substitute LHS of Eq. \ref{eq:1708642} and LHS of Eq. \ref{eq:5168370} and LHS of Eq. \ref{eq:4037937} into Eq. \ref{eq:3843569}; yields Eq. \ref{eq:6759349}. \begin{equation} \frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2} \label{eq:6759349} \end{equation} Divide both sides of Eq. \ref{eq:6759349} by $$V$$; yields Eq. \ref{eq:8713399}. \begin{equation} \frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2} \label{eq:8713399} \end{equation} Eq. \ref{eq:8713399} is one of the final equations.