11.4 Exercise 17

Once you have a system of equations generated by the partial fraction decomposition, can you explain another method to solve it? For example if you had $\frac{7 x + 13}{3 x^{2} + 8 x + 15} = \frac{A}{x + 1} + \frac{B}{3 x + 5}$, we eventually simplify to $7 x + 13 = A \left(3 x + 5\right) + B \left(x + 1\right) .$ Explain how you could intelligently choose an $x$ -value that will eliminate either $A$ or $B$ and solve for $A$ and $B .$