中二數學題

1) 1 / (x-2y) + 1 / (x+2y) = (x+2y) + (x-2y) / (x-2y) (x+2y)
= 2x / (x^2 - 4y^2)

2) (a-b) / (a+b) + (a+b) / (a-b) = [(a-b)^2 + (a+b)^2] / a^2 - b^2
= [a^2 - 2ab + b^2 + a^2 + 2ab + b^2] / a^2 - b^2
= [2 (a^2 - b^2)] / a^2 - b^2
= a^2 - b^2

3) 1 - [(xy + y^2) / (x + y)^2] = 1 - [y(x+y) / (x+y)^2]
= 1 - [y / (x+y)]

4) 1 / [3(x-1)] + 2 / [5(1-x)] = (5 - 5x + 6x - 6) / [15 (x-1)(1-x)]
= (x-1) / [15 (x-1)(1-x)] = 1 / 15 (1-x)

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