Rút gọn biểu thức: `A=(x/(x-1)) + (2x)/(1-x^2)) – (1/(x+1))`

2 bình luận về “Rút gọn biểu thức: `A=(x/(x-1)) + (2x)/(1-x^2)) – (1/(x+1))`”

1. $\text{A = $\dfrac{x}{x-1}$ + $\dfrac{2x}{1-x²}$ – $\dfrac{1}{x+1}$ (ĐK: x $\neq$ ± 1)}$

   $\text{= $\dfrac{x}{x-1}$ – $\dfrac{2x}{x² – 1}$ – $\dfrac{1}{x+1}$}$

   $\text{= $\dfrac{x}{x-1}$ – $\dfrac{2x}{(x -1)(x+1)}$ – $\dfrac{1}{x+1}$}$

   $\text{= $\dfrac{x(x+1)}{(x-1)(x+1)}$ – $\dfrac{2x}{(x -1)(x+1)}$ – $\dfrac{1.(x-1)}{x+1}(x-1)$}$

   $\text{= $\dfrac{x² + x – 2x – x + 1}{(x-1)(x+1)}$}$

   $\text{= $\dfrac{x² – 2x + 1}{(x-1)(x+1)}$}$

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

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

   $\text{= $\dfrac{x-1}{x+1}$}$

   Trả lời
2. A = x/[x-1] + [2x]/[1-x^2] – 1/[x+1] (ĐK: x \ne +-1)

   A = x/[x-1] – [2x]/[x^2-1] – 1/[x+1]

   A = [x(x+1)]/[(x-1)(x+1)] – [2x]/[(x-1)(x+1)] – [x-1]/[(x-1)(x+1)]

   A = [x^2+x-2x-x+1]/[(x-1)(x+1)]

   A = [x^2-2x+1]/[(x-1)(x+1)]

   A = [(x-1)^2]/[(x-1)(x+1)]

   A = [x-1]/[x+1]

   @BadMo od

   Trả lời