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)
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)
(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)] (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...

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(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)

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