Thực hiện phép tính: $\frac{x+3}{x+1}$- $\frac{2x-1}{x-1}$- $\frac{x-3}{x^{2}-1}$

Đáp án:

 `(x + 3)/(x + 1) – (2x – 1)/(x – 1) – (x – 3)/(x^2  – 1)`

`= (x + 3)/(x + 1) – (2x – 1)/(x – 1) – (x – 3)/[(x – 1)(x + 1)]`

`= [(x + 3)(x – 1)]/[(x – 1)(x + 1)] – [(2x – 1)(x + 1)]/[(x – 1)(x + 1)] – (x – 3)/[(x – 1)(x + 1)]`

`= [(x + 3)(x – 1) – (2x – 1)(x + 1) – (x – 3)]/[(x – 1)(x + 1)]`

`= (x^2 + 3x – x – 3 – 2x^2 + x – 2x + 1 – x + 3)/[(x – 1)(x + 1)]`

`= (-x^2 + 1)/[(x – 1)(x + 1)]`

`= [-(x – 1)(x + 1)]/[(x – 1)(x + 1)]`

`= -1`

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