CHAPTER 30
246
Then -3 = 8C, C=-|. Thus,
30.6
Thus,
Then -7 = 6C, C = -1.
Let x = 0.
Let x = -2.
Then l = -6A, A = -k. Let * = -3. Then
Then 2 = 12D, D=£.
Let x = l.
So jc
3 + 1 = A(x + 3)(x + 2)(x -l) + Bx(x + 2)(x -
and
30.7
Let
Then
Then -3 =
Let x = -3.
Let x = 2. Then 2=-20D, D = -^.
Then 3 = 30.4. A=&.
Let x = 3.
Let x = -2. Then -2 = 20C, C =.-•&.
So
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In
and
30.8
Multiply both sides by x\x + l), obtaining x-5 = Ax(x + 1) + B(x +
Let x = 0. Then -5 = B. Let * = -!. Then -6 = C. To find A, compare coefficients of
and
Thus,
x
2 on both sides of the equation: 0=A + C, A = -C = 6.
In
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In
Let
30.9
Let x = -2.
Then 2x = A(x - 2)(x + 2) + B(x + 2)+ C(x - 2)
2
.
To find A, equate coefficients of x
2 :
Then -4=16C. C=-i.
Thus,
and
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In
30.10
1) + CA-(A- + 3)(x - 1) + Dx(x + 3)(x + 2).
-26=-12B, S=f.
x
4 - I3x
2 + 36 = (x
2 - 9)(x
2 - 4) = (x - 3)(x + 3)(x + 2)(x - 2).
x = A(x + 3)(x + 2)(x - 2) + B(x - 3)0 + 2)(x - 2) + C(x - 3)(x +
3)(x -2) + D(x - 3)(x + 3)(x + 2).
-305. B=-k.
In
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in
1) + Cx
2 .
x = 2. Then 4 = 4fl, 5=1.
0 = A+ C, A = -C=\.
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