<s>[INST] Clarification on partial fraction expansion I would like to use the cover up method for the following equation.
$$\frac{1}{x^2(x+1.79)}$$
and it breaks down into
$$\frac{A}{x}\quad\frac{B}{x^2}\quad\frac{C}{(x + 1.79)}$$
I realize that you cover up $(x+1.79)$ to get $x = -1.79$ but what do you do for the other variables?
Thanks for your help.
 [/INST] With
$$\frac{1}{x^2(x+1.79)}=
\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x + 1.79}$$
the coefficients are calculated as follows
\begin{align}
& C =\lim_{x\to -1.79} \frac{x+1.79}{x^2(x+1.79)}=\frac1{1.79^2}\\
& B =\lim_{x\to 0} \frac{x^2}{x^2(x+1.79)}=-\frac1{1.79}\\
&A = \frac{x}{x^2(x+1.79)}-\frac {Bx}{x^2}- \frac {Cx}{x+1.79}=\frac1{1.79^2}
\end{align}
</s>