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Unformatted text preview: tiply the right side out and then collect all the like terms as
follows, 8 x 2  12 = Ax 2 + 2 Ax  6 A + Bx 2 + Cx
8 x 2  12 = ( A + B ) x 2 + ( 2 A + C ) x  6 A
Now, we need to choose A, B, and C so that these two are equal. That means that the coefficient
of the x2 term on the right side will have to be 8 since that is the coefficient of the x2 term on the
right side. Likewise, the coefficient of the x term on the right side must be zero since there isn’t
an x term on the left side. Finally the constant term on the right side must be 12 since that is the
constant on the left side.
We generally call this setting coefficients equal and we’ll write down the following equations. A+ B = 8
2A + C = 0
6 A = 12
Now, we haven’t talked about how to solve systems of equations yet, but this is one that we can
do without that knowledge. We can solve the third equation directly for A to get that A = 2 . We
can then plug this into the first two equations to get, 2+ B =8 Þ B=6 2 ( 2) + C = 0 Þ C = 4 So, the partial fraction decomposition for this expression is, 8 x 2  12
2
6x  4
= +2
2
x ( x + 2x  6) x x + 2x  6
[Return to Problems] 3x + 7 x  4
3 (b) (x 2 + 2) 2 Here is the form of the partial fractio...
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 Spring '12
 MrVinh

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