In practice, circuits are often combinations of series and parallel connections, sometimes nested. You can simplify these step by step by replacing portions with equivalent components until only a single equivalent element remains.
Example setup. A resistor \(R_1\) is in series with a parallel branch made of \(R_2\) and \(R_3\).
1) First reduce the parallel branch:
\[
\frac{1}{R_{2\parallel 3}}=\frac{1}{R_2}+\frac{1}{R_3}
\quad\Longrightarrow\quad
R_{2\parallel 3}=\frac{R_2R_3}{R_2+R_3}.
\]
2) Then add the series resistor:
\[
\boxed{\,R_\text{eq}=R_1+R_{2\parallel 3}
=R_1+\frac{R_2R_3}{R_2+R_3}\, }.
\]
Example Problem:
Two resistors \(27\,\Omega\) and \(14\,\Omega\) are in parallel; that branch is in series with \(56\,\Omega\).
\[
R_{2\parallel 3}=\frac{27\cdot14}{27+14}=\frac{378}{41}\approx 9.22\,\Omega,
\qquad
R_\text{eq}=56+9.22\approx \boxed{65.2\,\Omega}.
\]