  Let $B \subseteq A$ be an extension of finite dimensional algebras. We
provide a sufficient condition for the existence of triangle equivalences of
singularity categories (resp. Gorenstein defect categories) between $A$ and
$B$. This result is applied to trivial extensions, Morita rings and triangular
matrix algebras to give several reduction methods on singularity categories and
Gorenstein defect categories of algebras.
