Once you have a system of equations generated by the partial fraction decomposition, can you explain another

Question:

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 we eventually simplify to 7x + 13 = A(3x + 5) + B(x+1). Explain how you could intelligently choose an x-value that will eliminate either A or B and solve for A and B.