Unformatted text preview: ion as the weapon of choice to solve this system. From A + C = 0, we
get A = −C ; from 4B + 4D = 0, we get B = −D. Substituting these into the remaining two
equations, we get
√
√
−2C 2 − D − 2C 2 + D = 8
√
√
−4C − 2D 2 + 4C − 2D 2 = 0
or
√
−4C √2 = 8
−4D 2 = 0
√
√
We get C = − 2 so that A = −C = 2 and D = 0 which means B = −D = 0. Our ﬁnal
answer is
√
√
8x2
x2
x2
√
√
=
−
x4 + 16
x2 − 2x 2 + 4 x2 + 2 x 2 + 4 8.6 Partial Fraction Decomposition 529 As we stated at the beginning of this section, the technique of resolving a rational function into
partial fractions is a skill needed for Calculus. However, we hope to have shown you that it is worth
doing if, for no other reason, it reinforces a hefty amount of algebra. In the end, if you take only
one thing away from this section, it’s that
8
8
8
= 2−
−9
x
9
For if the above were true, this section wouldn’t be here.
x2 530 8.6.1 Systems of Equations and Matrices Exercises 1. Find o...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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