Consider

The fraction can be broken down into + with A and B to be determined.

You can solve this using algebra as it's normally taught. However since the denominator consists of linear factors, then there's a formula that says A = 1/(2-1) = 1 and B = 1/(1 - 2) = -1. More generally if you have , then A = (b - a) and B = (a - b).

Your first puzzle is given an expression , break it up into the individual fractions and determine what A, B and C arewithout first using algebra(you might see a pattern in connection with the previous example).

Your second puzzle is given the expression , again break it up into the individual fractions and determine what A, B and C are in this case (please note I take exception withSchaum'sthat says some quadratics are irreducible since they all

are reducible as the last problem illustrates).

The point to this exercise is that it's far simpler to do these problems by formula than by algebra (also note that this particular method works with fractions with one as the numerator and only linear factors in the denominator).

Okay sharpen your pencils and go to work.