Asymptotics of Multivariate Generating Series

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I am new to Sage and I need to find the asymptotic form of the series coefficients of the following generating function:

F(t,x,z) = (1 + t*x - t*x*z)/(1 - t - t^2*x - t*x*z + t^2*x*z)

In other words, in the Taylor expansion of the function in terms of the variable $t$, I am interested in the asymptotic form of the coefficient of the term $t^L\ x^N\ z^B$ in the limit of large $L$, $N$, and $B$.