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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: 3/(x+2).(x+5)+5/(x+5).(x+10)+7/(x+10).(x+17)=x/(x+2).(x+17)

Tháng Một 18, 2023 Toán học 2 Comments 0 views

Toán Lớp 7: 3/(x+2).(x+5)+5/(x+5).(x+10)+7/(x+10).(x+17)=x/(x+2).(x+17)

Comments ( 2 )

  1. catlantuong
    catlantuong
    18 Tháng Một, 2023 at 8:33 sáng
    Reply
    3/[(x+2)(x+5)] + 5/[(x+5)(x+10)] + 7/[(x+10)(x+17) ]= x/[(x+2)(x+17)]
    ĐK: x ne -2;xne-5; x ne-10;xne-17
    => 1/(x+2) – 1/(x+5) + 1/(x+5) – 1/(x+10) + 1/(x+10) – 1/(x+17) = x/[(x+2)(x+17)]
    => 1/(x+2) – 1/(x+17) = x/[(x+2)(x+17)]
    => (x+17)/[(x+2)(x+17)]  -(x+2)/[(x+2)(x+17)] =      x/[(x+2)(x+17)]
    => [(x+17 – x -2)]/[(x+2)(x+17)] =   (x)/[(x+2)(x+17)]
    => x + 17 – x – 2 =x
    => 17 -2 =x
    => x= 15 (thỏa mãn)
    Vậy x=15
     

  2. huongtructram
    huongtructram
    18 Tháng Một, 2023 at 8:32 sáng
    Reply
    $\begin{array}{l} \frac{3}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{5}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{7}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ DK:\,\,\,\left\{ \begin{array}{l} x \ne – 2\\ x \ne – 5\\ x \ne – 10\\ x \ne – 17 \end{array} \right.\\ pt \Leftrightarrow \frac{{x + 5 – \left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{{x + 10 – \left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{{x + 17 – \left( {x + 10} \right)}}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow \frac{1}{{x + 2}} – \frac{1}{{x + 5}} + \frac{1}{{x + 5}} – \frac{1}{{x + 10}} + \frac{1}{{x + 10}} – \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow \frac{1}{{x + 2}} – \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow x + 17 – x – 2 = x\\ \Leftrightarrow x = 15\,\,\,\left( {tm} \right).\\ Vay\,\,\,x = 15. \end{array}$
     

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222-9+11+12:2*14+14 = ? ( )

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