The main theorem is that if A is a central simple flexible algebra, with an identity, of arbitrary dimension over a field F of characteristic not 2, and if A is Lie-admissible and ${A^ + }$ is associative, then ${\text {ad}}\;(A)â = [A,A]/F$ is a simple Lie algebra. It is shown that this theorem applies to simple nodal noncommutative Jordan algebras of arbitrary dimension, and hence that such an algebra A also has derived algebra ${\text {ad}}\;(A)â$ simple.