Thực hiện phép trừ x^2 – 1/2x^2 – 4x + 2 – x+3/2x + 2 ( GIÚP EM )

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1. Đáp án:

   Bạn tham khảo nhé 

   Giải thích các bước giải:

   $\frac{x^2 – 1}{2x^2 – 4x + 2} – \frac{x + 3}{2x + 2}$ $\\$ $= \frac{x^2 – 1}{2(x^2 – 2x + 1)} – \frac{x + 3}{2(x + 1)}$ $\\$ $ = \frac{x^2 – 1}{2(x – 1)^2} – \frac{x + 3}{2(x + 1)}$ $\\$ $MTC = 2(x – 1)^2(x + 1)$ $\\$ $ = \frac{(x^2 – 1)(x + 1)}{2(x – 1)^2(x + 1)} – \frac{(x + 3)(x – 1)^2}{2(x – 1)^2(x + 1)}$ $\\$ $= \frac{(x^2 – 1)(x + 1) – (x + 3)(x – 1)^2}{2(x – 1)^2(x + 1)}$ $\\$ $= \frac{x^3 + x^2 – x – 1 – (x + 3)(x^2 – 2x + 1)}{2(x – 1)^2(x + 1)}$ $\\$ $= \frac{x^3 + x^2 – x – 1 – (x^3 – 2x^2 + x + 3x^2 – 6x + 3)}{2(x – 1)^2(x +1)}$

   $= \frac{x^3 + x^2 – x – 1 – x^3 + 2x^2 – x – 3x^2 + 6x – 3}{2(x – 1)^2(x + 1)}$ $\\$ $= \frac{4x – 4}{2(x – 1)^2(x + 1)} = $ $\frac{4(x – 1)}{2(x – 1)(x – 1)(x + 1) }=$ $\frac{4}{2(x – 1)(x + 1)} = $$\frac{2}{(x – 1)(x + 1)}$

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2. `ĐK: x ne +-1`

   `(x^2 – 1)/(2x^2 – 4x + 2) – (x + 3)/(2x + 2)`

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

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

   `= ((x + 1)^{2} – (x + 3)(x – 1))/(2(x – 1)(x + 1))`

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

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

   `= -2/(2(x – 1)(x + 1))`

   `= -1/(x^2 – 1)`

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