F.2 Algebraic fractions

wai

2010-10-06 1:47 am

Simplify the following expression with steps.
1. 2x-x^2/3y divide 2-x/5y^2-2y
2. y/4(x+y) - 8+y/4(x+y)
3. x/x-y + y/y-x
4. 2x-5/2(x-1) - 3x/2(1-x)
5. - t/2(4t-9) - 3/4(9-4t)
6. 3a/a-b - b/3b-3a

* remember don't skip any needed steps.

更新1:

only need to do the last two questions.

回答 (1)

用戶2053

2010-10-06 2:46 am

✔ 最佳答案

1)

2x-x^2/3y divide 2-x/5y^2-2y= [ (2x - x^2) / (3y) ] / [ (2-x) / (5y^2 - 2y) ]= (2x - x^2)(5y^2 - 2y) / [ (3y) (2 - x) ]= x(2 - x) y(5y - 2) / [ (3y) (2 - x) ]= x(5y - 2) / 32)y/4(x+y) - 8+y/4(x+y)= [ y - (8+y) ] / [4(x+y)]= - 8 / [4(x+y)]= - 2 / (x+y)3) x/x-y + y/y-x= x/(x-y) - y(x-y)= (x-y) / (x-y)= 14)2x-5/2(x-1) - 3x/2(1-x)= (2x-5) / [2(x-1)] + 3x / [2(x-1)]= (5x - 5) / [2(x-1)]= 5(x-1) / [2(x-1)]= 5/25)- t/2(4t-9) - 3/4(9-4t)= - 2t / [4(4t-9)] + 3 / [4(4t-9)]= (3 - 2t) / [4(4t-9)]6) 3a/a-b - b/3b-3a= 9a / [ 3(a - b) ] + b / [3(a - b)]= (9a + b) / [3(a - b)]

2010-10-05 23:51:12 補充：
5)

- t/2(4t-9) - 3/4(9-4t)

= (-t/2)(4t-9) - (3/4)(9-4t)

= (-t/2)(4t-9) + (3/4)(4t-9)

= (4t-9)(-t/2 + 3/4)

= (4t-9)(3-2t)/4

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