Page 45 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

When x = 1, 1 + 1 = 0 + 3A + B(0)
2 = 3A
1 A = 2
3
When x = –2, –8 + 1 = 0 + A(0) + B(–3)
–7 = –3B
B = 7
3
3
Hence, x + 1 = x – 1 + 2 + 7
(x – 1)(x + 2) 3(x – 1) 3(x + 2)

Exercise 1.7

Express each of the following expressions in partial fractions.

1. 2x + 4 2. x – 4 3. 3
(x + 1)(x + 2) (x + 2)(x – 1) x – 9
2

4. x 5. x + 1 6. x + 3
2
2
x – 1 x – 4 x + 5x + 4
2
2
7. 4x + 10 8. 4x + 2 9. x – 2x + 4
(2 + x)(3 + x)(4 + x) (x + 2)(x – 1) 2x(x – 3)(x + 1)
2
2
10. x – 4 11. x 12. 9
x(x + 1)(x + 3) (1 + x) 2 (x – 1)(x + 2) 2

2
2
13. 3x + x – 2 14. x – 1 15. 1
2
(2x – 1)(x – 2) 2 x (2x + 1) x (x – 1)
2
2
2
2
2
16. x + 1 17. x + x – 1 18. 2x + 3x + 2
2
2
x – 1 (x + 1)(x + 2) x + 3x + 2
3
3
19. x + x + 1 20. x + 3 21. 2x – 1
(x + 1) 2 (x + 1)(x – 1) (x + 2)(x + 1)
2
22. x + 1 23. 3x 24. 1
2
2
x(x + x + 1) (x – 1)(x + x + 1) (x – 1)(x – x + 1)
2
25. x
(x + 1)(x – 1) 3

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01a STPM Math T T1.indd 42 3/28/18 4:20 PM