Thực hiện các phép tính:
a) \((\dfrac{x}{x+1}+1):(1-\dfrac{3x^2}{1-x^2})\) b) \((x^2-1)(\dfrac{1}{x-1}-\dfrac{1}{x+1}-1)\)
a) \((\dfrac{x}{x+1}+1):(1-\dfrac{3x^2}{1-x^2})\) = \(\dfrac{2x+1}{x+1}:\dfrac{1-4x^2}{1-x^2}\)
= \(\dfrac{2x+1}{x+1}.\dfrac{1-x^2}{1-4x^2}\)= \(\dfrac{(2x+1)(1-x)(1+x)}{(x+1)(1-2x)(1+2x)}\)= \(\dfrac{1-x}{1-2x}\)
b) \((x^2-1)(\dfrac{1}{x-1}-\dfrac{1}{x+1}-1)\)
= \((x^2-1)[\dfrac{(x+1)-(x-1)-(x^2-1)}{x^2-1}]\)
= \((x^2-1).\dfrac{3-x^2}{x^2-1}=3-x^2\)
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