F4 maths

你2條題目的括號都放錯位置
我已經幫你更正,看看是不是你想問的問題

1. A/(x+1) + B/(x-2) ≡ (4x-5)/(x^2-x-2)

(4x-5)/(x^2-x-2) = (4x-5)/[(x+1)(x-2)]

所以,A/(x+1) + B/(x-2) ≡ (4x-5)/[(x+1)(x-2)]
[A * (x-2) + B * (x+1)] / [(x+1)(x-2)] ≡ (4x-5)/[(x+1)(x-2)]

A * (x-2) + B * (x+1) ≡ (4x-5)
當 x = -1,
-3A = -4 - 5
A = 3
當 x = 2,
3B = 8 - 5
B = 1

所以,A = 3, B = 1

2. 28/(x^2+x-12) ≡ 2A/(x+4) +4B/(x-3)

28/(x^2+x-12) = 28/[(x+4)(x-3)]

所以,28/[(x+4)(x-3)] ≡ 2A/(x+4) +4B/(x-3)
28/[(x+4)(x-3)] ≡ [2A * (x-3) + 4B * (x+4)]/[(x+4)(x-3)]

2A * (x-3) + 4B * (x+4) = 28
當 x = -4,
-14A = 28
A = -2
當 x = -3,
28B = 28
B = 1

所以,A = -2, B = 1