Alg_Complete

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Unformatted text preview: Example 2 Determine the partial fraction decomposition of each of the following. 8 x 2 - 12 (a) [Solution] x ( x2 + 2 x - 6) (b) 3x3 + 7 x - 4 (x 2 + 2) 2 [Solution] Solution 8 x 2 - 12 (a) x ( x2 + 2 x - 6) In this case the x that sits in the front is a linear term since we can write it as, x = x+0 and so the form of the partial fraction decomposition is, 8 x 2 - 12 A Bx + C = +2 2 x ( x + 2x - 6) x x + 2x - 6 ( ) Now we’ll use the fact that the LCD is x x 2 + 2 x - 6 and add the two terms together, A ( x + 2 x - 6 ) + x ( Bx + C ) 8 x 2 - 12 = 2 x ( x + 2x - 6) x ( x2 + 2x - 6) 2 © 2007 Paul Dawkins 276 http://tutorial.math.lamar.edu/terms.aspx College Algebra Next, set the numerators equal. 8 x 2 - 12 = A ( x 2 + 2 x - 6 ) + x ( Bx + C ) This is where the process changes from the previous set of examples. We could choose x = 0 to get the value of A, but that’s the only constant that we could get using this method and so it just won’t work all that well here. What we need to do here is mul...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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