Partial Fraction Decomposition 

Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions. To decompose a fraction, you first factor the denominator. Let's work backwards from the example above. The denominator is x2 + x, which factors as x(x + 1). Then you write the fractions with one of the factors for each of the denominators. Of course, you don't know what the numerators are yet, so you assign variables (usually capital letters) for these unknown values: A/x + B/(x + 1) Then you set this sum equal to the simplified result: (3x + 2)/[x(x + 1)] = A/x + B/(x + 1) Multiply through by the common denominator of x(x + 1) gets rid of all of the denominators: multiply each term by [x(x + 1)] / 1 3x + 2 = A(x + 1) + B(x)