1 25x-15 ———- – ————- x-5x^2 25x^2 -1

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1. Ta có

   $\dfrac{1}{x-5x^2} – \dfrac{25x-15}{25x^2 – 1} = \dfrac{1}{x(1-5x)} – \dfrac{25x-15}{(5x-1)(5x+1)}$

   $= \dfrac{1 + 5x}{x(1-5x)(1+5x)} + \dfrac{x(25x-15)}{x(1-5x)(1+5x)}$

   $= \dfrac{1 + 5x + 25x^2 – 15x}{x(1-5x)(1+5x)}$

   $= \dfrac{25x^2 – 10x + 1}{x(1-5x)(1+5x)}$

   $= \dfrac{(1-5x)^2}{x(1-5x)(1+5x)}$

   $= \dfrac{1-5x}{x(1+5x)}$

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