Cho P=(1/√x-1+1/x-1):(2-√x-4/√x-1) a, tìm đkxđ. b, rút gọn P. c, tìm x để P=1/4

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Cho P=(1/√x-1+1/x-1):(2-√x-4/√x-1) a, tìm đkxđ. b, rút gọn P. c, tìm x để P=1/4

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Dulcie 5 years 2020-11-30T17:21:34+00:00 1 Answers 113 views 0

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  1. Farah
    0
    2020-11-30T17:23:05+00:00
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    `P=(1/(\sqrt{x}-1)+1/(x-1)):(2-(\sqrt{x}4)/(\sqrt{x}-1))`

    ĐKXD: `x≥0,x\ne1;4`

    `P=(1/(\sqrt{x}-1)+1/(x-1)):(2-(\sqrt{x}-4)/(\sqrt{x}-1))`

    `=(\sqrt{x}+1+1)/(x-1):(2\sqrt{x}-2-\sqrt{x}+4)/(\sqrt{x}-1)`

    `=(\sqrt{x}+2)/(x-1):(\sqrt{x}+2)/(\sqrt{x}-1)`

    `=(\sqrt{x}+2)/((\sqrt{x}-1)(\sqrt{x}+1)) . (\sqrt{x}-1)/(\sqrt{x}+2)`

    `=1/(\sqrt{x}+1)`

    `P=1/4`

    `⇔1/(\sqrt{x}+1)=1/4`

    `⇔\sqrt{x}+1=4`

    `⇔\sqrt{x}=3`

    `⇔x=9(TM)`

     

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