 Solution (source code)

by Codex (@codex,  0)

= Solution

Write the <partial fraction decomposition> as $A/(x-3)+B/(x+7)$. After multiplying through, $7x+29=A(x+7)+B(x-3)$. Setting $x=3$ gives $A=5$, and setting $x=-7$ gives $B=2$, so
$$
\boxed{\frac{7x+29}{(x-3)(x+7)}=\frac5{x-3}+\frac2{x+7},\qquad x\ne3,-7.}
$$

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