Giải phương trình:
2/(x - 14) - 5/(x - 13) = 2/(x - 9) - 5/(x - 11)
ĐKXĐ : x <>14; x <>13; x <>9 ; x <>11
<=> 2(x-13)(x-9)(x-11)/ (x-14)(x-13)(x-9)(x-11) - 5(x-14)(x-9)(x-11)/(x - 13)(x-14)(x-9)(x-11) = 2 (x-14)(x-13)(x-11) /(x - 9)x-14)(x-13)(x-11)- 5 (x-14)(x-13)(x-9)/(x - 11)(x - 13)(x-14)(x-9)
<=> 2(x-13)(x-9)(x-11) - 5(x-14)(x-9)(x-11) = 2 (x-14)(x-13)(x-11) - 5 (x-14)(x-13)(x-9)
<=> (2x - 26)(x^2 -11x-9x+99) - (5x-60)(x^2-11x-9x+99) = (2x -28)(x^2 -11x -13x +143)-(5x-60)(x^2-9x-13x+117)
<=>(x^2 -11x-9x+99)(2x-26-5x+60) = (2x-28)(x^2 -25x+143)-(5x-60)(x^2 -22x+117)
<=> (x^2 -20x+99)(-3x + 34) = 2x^3 -50x^3 + 286x -28x^2 + 700x - 4004 + 5x^3 +60x^2 + 110x^2-1320x - 585x+7020
<=> -3x^3 +34x^2 +60x-680x-297x+3366 = 2x^3 -50x^3 + 286x -28x^2 + 700x - 4004 + 5x^3 +60x^2 + 110x^2-1320x - 585x+7020
<=> -3x^3 +34x^2 -917x + 3366 = -43x^3 +142x^2-919x + 3016
<=> -3x^3 +34x^2 -917x + 3366 +43x^3 -142x^2+919x - 3016 = 0
<=> -40x^3+ 881x^2 +2x +350 = 0