  We establish an infinitesimal variant of Guo-Jacquet trace formula for the
case of a central simple algebra over a number field $F$ containing a quadratic
field extension $E/F$. It is an equality between a sum of geometric
distributions on the tangent space of some symmetric space and its Fourier
transform. To prove this, we need to define an analogue of Arthur's truncation
and then use the Poisson summation formula. We describe the terms attached to
regular semi-simple orbits as explicit weighted orbital integrals. To compare
them to those for another case studied in our previous work, we state and prove
the weighted fundamental lemma at the infinitesimal level by using Labesse's
work on the base change for $GL_n$.
