Toán 9 Rút gọn biểu thức

Ann Lee

Ann Lee

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14 Tháng tám 2017
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(x−y2y−x−x2+y2+y−2x2−xy−2y2):4x4+4x2y+y2−4x2+y+xy+x\left ( \frac{x-y}{2y-x}-\frac{x^{2}+y^{2}+y-2}{x^{2}-xy-2y^{2}} \right ):\frac{4x^{4}+4x^{2}y+y^{2}-4}{x^{2}+y+xy+x}
=[x−y2y−x−x2+y2+y−2(x+y)(x−2y)]:(2x2+y)2−4(x+1)(x+y)=\left [\frac{x-y}{2y-x}-\frac{x^{2}+y^{2}+y-2}{(x+y)(x-2y)} \right ]:\frac{(2x^{2}+y)^{2}-4}{(x+1)(x+y)}
=−(x−y)(x+y)−(x2+y2+y−2)(x+y)(x−2y):(2x2+y−2)(2x2+y+2)(x+y)(x+1)=\frac{-(x-y)(x+y)-(x^{2}+y^{2}+y-2)}{(x+y)(x-2y)}:\frac{(2x^{2}+y-2)(2x^{2}+y+2)}{(x+y)(x+1)}
=−2x2+2−y(x+y)(x−2y).(x+y)(x+1)(2x2+y−2)(2x2+y+2)=\frac{-2x^{2}+2-y}{(x+y)(x-2y)}.\frac{(x+y)(x+1)}{(2x^{2}+y-2)(2x^{2}+y+2)}
=x+1(2y−2)(2x2+y+2)=\frac{x+1}{(2y-2)(2x^{2}+y+2)}
 
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