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

Toán Lớp 9: cho biểu thức B=x/x+3 + 2x-1/x-3 – 2x^2-x-3/x^2-9 với x khác 3;x khác -3 chứng minh B=x/x-3

Toán Lớp 9: cho biểu thức B=x/x+3 + 2x-1/x-3 – 2x^2-x-3/x^2-9 với x khác 3;x khác -3 chứng minh B=x/x-3

Comments ( 2 )

  1. ~ Gửi bạn nhea ~
    B = x/(x+3) + (2x-1)/(x-3) – (2x^2-x-3)/(x^2-9)
    = x/(x+3) + (2x-1)/(x-3) – (2x^2-x-3)/((x-3)(x+3))
    = (x(x-3)+(x+3)(2x-1)-(2x^2-x-3))/((x-3)(x+3))
    = (x^2-3x+2x^2-x+6x-3-2x^2+x+3)/((x-3)(x+3))
    = ((x^2-2x^2+2x^2)+(6x-3x+x-x)+(3-3))/((x-3)(x+3))
    = (x^2+3x)/((x-3)(x+3))
    = (x(x+3))/((x-3)(x+3))
    = x/(x-3)
    ->đpcm

  2. ***Lời giải***
    ĐKXĐ:xne3;xne-3
    B=\frac{x}{x+3}+\frac{2x-1}{x-3}-\frac{2x^2-x-3}{x^2-9}
    =\frac{x(x-3)+(2x-1)(x+3)-(2x^2-x-3)}{(x-3)(x+3)}
    =\frac{x^2-3x+2x(x+3)-(x+3)-(2x^2-x-3)}{(x-3)(x+3)}
    =\frac{x^2-3x+2x^2+6x-x-3-2x^2+x+3}{(x-3)(x+3)}
    =\frac{(x^2+2x^2-2x^2)+(-3x+6x)+(-x+x)+(-3+3)}{(x-3)(x+3)}
    =\frac{x^2+3x}{(x-3)(x+3)}
    =\frac{x(x+3)}{(x-3)(x+3)}
    =\frac{x}{x-3}

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