Rút gọn các phân thức sau: a, (2x^2+2x)(x-2)^2/(x^3-4x)(x+1) b, x^3-x^2y+xy^2/x^3+y^3 c, a^2+b^2-c^2+2ab/a^2-b^2+c^2+2ab d, 2x^3-7x^2-12x+45/3x^3-1

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1. a) Ta có

   $\dfrac{(2x^2+2x)(x-2)^2}{(x^3-4x)(x+1)} = \dfrac{2x(x+1)(x-2)^2}{x(x^2-4)(x+1)}$

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

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

   b) Ta có

   $\dfrac{x^3-x^2y+xy^2}{x^3 + y^3} = \dfrac{x(x^2 -xy + y^2)}{(x+y)(x^2 – xy + y^2)}$

   $= \dfrac{x}{x+y}$

   d) Ta có

   $\dfrac{2x^3 – 7x^2 – 12x + 45}{3x^3 – 19x^2 + 33x – 9} = \dfrac{(x-3)(2x^2 -x -15)}{(x-3)(3x^2 -10x + 3)}$

   $= \dfrac{(x-3)(2x+5)}{(x-3)(3x-1)}$

   $= \dfrac{2x+5}{3x-1}$

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