= Solution
Let $i:L\hookrightarrow M$, $j:L\hookrightarrow N$, $r:M\hookrightarrow K$, and $s:N\hookrightarrow K$ be the inclusions. The <Mayer–Vietoris sequence> is the <long exact sequence in homology>
$$
\cdots\longrightarrow H_k(L)
\xrightarrow{(i_*,-j_*)}
H_k(M)\oplus H_k(N)
\xrightarrow{r_*+s_*}
H_k(K)
\xrightarrow{\partial_*}
H_{k-1}(L)
\longrightarrow\cdots.
$$
The same sequence continues through degree zero, or uniformly in all degrees when written with <reduced homology>.
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