化简再求值:(x-2)/(x^2-9){1+[2x-7/(x^2-4x+4)]}/[1/(x+3)] (其中x=3/4)
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化简再求值:(x-2)/(x^2-9){1+[2x-7/(x^2-4x+4)]}/[1/(x+3)] (其中x=3/4)
![化简再求值:(x-2)/(x^2-9){1+[2x-7/(x^2-4x+4)]}/[1/(x+3)] (其中x=3/4)](/uploads/image/z/19648352-56-2.jpg?t=%E5%8C%96%E7%AE%80%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A%28x-2%29%2F%28x%5E2-9%29%7B1%2B%5B2x-7%2F%28x%5E2-4x%2B4%29%5D%7D%2F%5B1%2F%28x%2B3%29%5D+%28%E5%85%B6%E4%B8%ADx%3D3%2F4%29)
(x-2)/(x^2-9){1+[2x-7/(x^2-4x+4)]}/[1/(x+3)] (其中x=3/4)
(x-2)/(x^2-9){1+[2x-7/(x^2-4x+4)]}/[1/(x+3)]
= (x-2)/[(x+3)(x-3)]{1+[2x-7/(x-2)^2]}(x+3)
= (x-2)/(x-3){1+[2x-7/(x-2)^2]}
= (x-2)[1+2x-7/(x-2)^2]/(x-3)
= [(1+2x)(x-2)^2 - 7]/[(x-3)(x-2)]
= [x^2 -4x +4 + 2x^3 -8x^2 +8x - 7]/[(x-3)(x-2)]
= [2x^3 -7x^2 +4x -3]/[(x-3)(x-2)]
= [2x^3 - 6x^2 - x^2 + 3x + x-3]/[(x-3)(x-2)]
= [(x-3)(2x^2 -x +1)]/[(x-3)(x-2)]
= (2x^2 - x + 1)/(x-2)
= [2(3/4)^2 - 3/4 + 1]/(3/4 - 2)
= [9/8 + 1/4]/(-5/4)
= -11/10
(x-2)/(x^2-9){1+[2x-7/(x^2-4x+4)]}/[1/(x+3)]
= (x-2)/[(x+3)(x-3)]{1+[2x-7/(x-2)^2]}(x+3)
= (x-2)/(x-3){1+[2x-7/(x-2)^2]}
= (x-2)[1+2x-7/(x-2)^2]/(x-3)
= [(1+2x)(x-2)^2 - 7]/[(x-3)(x-2)]
= [x^2 -4x +4 + 2x^3 -8x^2 +8x - 7]/[(x-3)(x-2)]
= [2x^3 -7x^2 +4x -3]/[(x-3)(x-2)]
= [2x^3 - 6x^2 - x^2 + 3x + x-3]/[(x-3)(x-2)]
= [(x-3)(2x^2 -x +1)]/[(x-3)(x-2)]
= (2x^2 - x + 1)/(x-2)
= [2(3/4)^2 - 3/4 + 1]/(3/4 - 2)
= [9/8 + 1/4]/(-5/4)
= -11/10
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