We could choose x 0 to get the value of a but thats

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Unformatted text preview: always do that. [Return to Problems] (b) 9 - 9x 2x + 7 x - 4 2 Okay, in this case we won’t put quite as much detail into the problem. We’ll first factor the denominator and then get the form of the partial fraction decomposition. 9 - 9x 9 - 9x A B = = + 2 x + 7 x - 4 ( 2 x - 1)( x + 4 ) 2 x - 1 x + 4 2 © 2007 Paul Dawkins 273 http://tutorial.math.lamar.edu/terms.aspx College Algebra In this case the LCD is ( 2 x - 1) ( x + 4 ) and so adding the two terms back up give, A ( x + 4 ) + B ( 2 x - 1) 9 - 9x = 2x + 7 x - 4 ( 2 x - 1)( x + 4 ) 2 Next we need to set the two numerators equal. 9 - 9 x = A ( x + 4 ) + B ( 2 x - 1) Now all that we need to do is correctly pick values of x that will make one of the terms zero and solve for the constants. Note that in this case we will need to make one of them a fraction. This is fairly common so don’t get excited about it. Here is this work. x = -4 : 45 = -9 B 1 x= : 2 9 = 2 æ9ö Aç ÷ è2ø Þ B = -5 Þ A =1 The partial fraction decomposition for this expression is,...
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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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