Alg_Complete

# We will always do that return to problems b 9 9x 2x

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Unformatted text preview: r, but since the subject needs to be covered and this was a fairly short chapter it seemed like as good a place as any to put it. So, let’s start with the following. Let’s suppose that we want to add the following two rational expressions. 8 ( x - 4) 5 ( x + 1) 8 5 = x + 1 x - 4 ( x + 1)( x - 4 ) ( x + 1)( x - 4 ) = 8 x - 32 - ( 5 x + 5) ( x + 1)( x - 4 ) = 3 x - 37 ( x + 1)( x - 4 ) What we want to do in this section is to start with rational expressions and ask what simpler rational expressions did we add and/or subtract to get the original expression. The process of doing this is called partial fractions and the result is often called the partial fraction decomposition. The process can be a little long and on occasion messy, but it is actually fairly simple. We will start by trying to determine the partial fraction decomposition of, P ( x) Q ( x) where both P(x) and Q(x) are polynomials and the degree of P(x) is smaller than the degree of Q(x). Partial fractions can only be done if the degree of the numerator is strictly less than the degree of the denominator. That is important to remember. So, once we’ve determined that partial fractions can be done we factor t...
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