We wish to write x + 3 (x − 3)(x + 1) as a sum a x − 3 + b x + 1 . let’s find a and b. set the two expressions equal and clear denominators (that is, multiply through by (x − 3)(x + 1) and cancel (x − 3)’s and (x + 1)’s as much as possible). plug in x = 3 and solve for a. use the same idea to find b. check your work by adding the two fractions together.