Page 26 - mathsvol1ch1to3ans

26

1 2
When x = 1, C= When x = −2, D=
6 15
When x = 0, 2B= 2C − D

2 2
= −
6 15

1
B =
10
When x = −1, 2A= −1 + 2B − 2C + 4D

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1 1 8 3
= −1 + − + = −
5 3 15 5
x 1 − 3x 1 2
Hence = + +
2
2
(x + 1)(x − 1)(x + 2) 10(x + 1) 6(x − 1) 15(x + 2)
x
4.
(x − 1) 3
x A B C
Let = + +
(x − 1) 3 x − 1 (x − 1) 2 (x − 1) 3
2
Then x = A(x − 1) + B(x − 1) + C
When x = 1, C = 1

When x = 0, A - B = −1

When x = −1, 4A -2B = −2 ⇒ 2A - B = −1

Solving we get A = 0,B = 1,C = 1.
x 1 1
Hence = +
(x − 1) 3 (x − 1) 2 (x − 1) 3
1
5.
x − 1
4
1 A B Cx + D
Let = + +
2
4
x − 1 x − 1 x + 1 x + 1
2
2
Then 1 = A(x + 1)(x + 1) + B(x − 1)(x + 1) + (Cx + D)(x + 1)(x − 1)
1
When x = 1, A =
4
1
When x = −1, B = −
4

1
When x = 0, D = −1 - A + B = −
2
1 -15A - 5B - 3D
When x = 2, C = −
2

= 0
1 1 1 1 1 1
Hence = − − = −
2
2
2
4
x − 1 4(x − 1) 4(x + 1) 2(x + 1) 2(x − 1) 2(x + 1)