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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
6x - 4
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