Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2​

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Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2​

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Liliana 4 weeks 2021-08-21T14:15:46+00:00 2 Answers 0 views 0

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    2021-08-21T14:17:03+00:00

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    Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2

    \huge\tt\underline\blue{Answer }

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    ⟹ \frac{5}{x - 2}  +  \frac{1}{x - 1} =  \frac{6}{x}

     ⟹  \frac{5(x - 1) + x - 2}{(x - 1)(x - 2)}  =  \frac{6}{x}

    ⟹ \frac{5x - 5 + x - 2}{(x - 2)(x - 1)}  =  \frac{6}{x}

    ⟹ \frac{6x - 7}{(x - 2)(x - 1)}  =  \frac{6}{x}

    ⟹ \frac{x(6x - 7)}{x(x - 1) - 2(x - 1)}  =  \frac{6}{x}

    ⟹ \frac{ {x}^{2}  - 7x}{ {x}^{2}  - x - 2x + 2}  =  \frac{6}{x}

    ⟹  {x}^{3}  - 7 {x}^{2}  = 6 {x}^{2}  - 18x + 12

    ⟹ {x}^{3}  - 13 {x}^{2}  + 18x - 12

    ⟹ {x}^{2} (x - 13) + 6(3x - 2)

    ⟹( {x}^{2}  + 6)(x - 13)(3x - 2) = 0

    ⟹ {x}^{2}  + 6 = 0

    ⟹x =± \sqrt{6}

    ⟹x - 13 = 0

    ⟹x = 13

    ⟹3x - 2 = 0

    ⟹x =  \frac{2}{3}

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    HOPE IT HELPS YOU..

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    0
    2021-08-21T14:17:11+00:00

    Answer:

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