`((x+1)/(2x-2) + 3/(x^2 -1) – (x+3)/(2x+2)) . (4x^2 – 4)/5`

Question

`((x+1)/(2x-2) + 3/(x^2 -1) – (x+3)/(2x+2)) . (4x^2 – 4)/5`

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Isabelle 4 tuần 2021-07-10T12:04:54+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-07-10T12:06:07+00:00

    Đáp án:

     

    Giải thích các bước giải:

    `((x+1)/(2x-2) + 3/(x^2 -1) – (x+3)/(2x+2)) . (4x^2 – 4)/5`

    ĐK: `x \ne +-1`

    `=[\frac{(x+1)^2}{2(x-1)(x+1)}+\frac{6}{2(x-1)(x+1)}-\frac{(x+3)(x-1)}{2(x-1)(x+1)}].\frac{4(x^2-1)}{5}`

    `=[\frac{x^2+2x+1+6-x^2-2x+3}{2(x-1)(x+1)}].\frac{4(x-1)(x+1)}{5}`

    `=\frac{10}{2(x-1)(x+1)}.\frac{4(x-1)(x+1)}{5}`

    `=4`

    0
    2021-07-10T12:06:19+00:00

    Đáp án + Giải thích các bước giải:

    `((x+1)/(2x-2)+(3)/(x^{2}-1)-(x+3)/(2x+2)).(4x^{2}-4)/(5)`

    `=((x+1)/(2(x-1))+(3)/((x-1)(x+1))-(x+3)/(2(x+1))).(4(x^{2}-1))/(5)`

    `=((x+1)^{2}+6-(x+3)(x-1))/(2(x-1)(x+1)).(4(x-1)(x+1))/(5)`

    `=(x^{2}+2x+1+6-(x^{2}+3x-x-3))/(2(x-1)(x+1)).(4(x-1)(x+1))/(5)`

    `=(x^{2}+2x+7-(x^{2}+2x-3))/(2(x-1)(x+1)).(4(x-1)(x+1))/(5)`

    `=(x^{2}+2x+7-x^{2}-2x+3)/(2(x-1)(x+1)).(4(x-1)(x+1))/(5)`

    `=(10)/(2(x-1)(x+1)).(4(x-1)(x+1))/(5)`

    `=4`

     

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