Please give me an example of this:

First, create a quadratic expression of the form ar- + br + c that can be factored. The easiest way to do this is to start with two linear factors of the form ar + b with a and /, both nonzero, and multiply them together. This will be your denominator. Then choose two numbers, p and q. They can be positive, negative or zero (but not both zero ) . Make the fraction pr + q aI- + ba + c and be sure that you choose p and q so that the fraction doesn't factor and cancel. We do not want anything like 31 + 6 3(x + 2) 12 - I - 6 (x + 2) (x - 3) I 3 to happen, that ruins the whole ideal This will be the fraction that the other student will need to decompose into its parts, the partial fraction decomposition. Note that the denominators of the two parts will be the factors of your original quadratic, so please don't provide them in your post