# F4 Maths Dividing Polynomials3

As follows.

Can you show the steps?

### 2 Answers

- 六呎將軍Lv 71 decade agoFavorite Answer
(1) (x - 8)/(x - 4) + (x - 5)/(x - 7) - 2

= (x - 4 - 4)/(x - 4) + (x - 7 + 2)/(x - 7) - 2

= [1 - 1/(x - 4)] + [1 + 2/(x - 7)] - 2

= 2/(x - 7) - 1/(x - 4)

(2) 2a/(a - 1) - (a - 1)/(a + 1) - (a + 1)/a

= [2(a - 1) + 2]/(a - 1) - (a + 1 - 2)/(a + 1) - 1 - 1/a

= 2 + 2/(a - 1) - 1 + 2/(a + 1) - 1 - 1/a

= 2/(a - 1) + 2/(a + 1) - 1/a

(3) (x + 2)/(x + 1) - (x + 3)/(x + 2) - (x + 5)/(x + 4) + (x + 6)/(x + 5)

= (x + 1 + 1)/(x + 1) - (x + 2 + 1)/(x + 2) - (x + 4 + 1)/(x + 4) + (x + 5 + 1)/(x + 5)

= 1 + 1/(x + 1) - 1 - 1/(x + 2) - 1 - 1/(x + 4) + 1 + 1/(x + 5)

= 1/(x + 1) - 1/(x + 2) - 1/(x + 4) + 1/(x + 5)

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- So MuchLv 71 decade ago
1.(x-8)/(x-4)+(x-5)/(x-7)-2

=[(x-8)(x-7)+(x-5)(x-4)]/[(x-4)(x-7)]-2

=(-24x+76)/[(x-4)(x-7)]-2

=(-x^2-2x+20)/(x-4)(x-7)

=-2(x-10)/[(x-4)(x-7)]//

2.2a/(a-1)-(a-1)/(a+1)-(a+1)/a

=(3 a^2+1)/((a-1) a (a+1))//

3.(x+2)/(x+1)-(x+3)/(x+2)-(x+5)/(x+4)+(x+6)/(x+5)

=(6 (x+3))/((x+1) (x+2) (x+4) (x+5))

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