先化简,再求值:[(4x^2+12x)/(x^2+x-6)/[(x-2)/(x+2)-(x+2)/(x-2)]其中x-3(2/1)
2个回答
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原式为:[(4x²+12x)/(x²+x-6)]/[(x-2)/(x+2)-(x+2)/(x-2)]
=4x(x+3)/(x+3)(x-2)÷[(x-2)²-(x+2)²]/(x+2)(x-2)
=4x/(x-2) ÷[(x-2+x+2)(x-2-x-2)]/(x+2)(x-2)
=4x/(x-2) ÷2x(﹣4)/(x+2)(x-2)
=4x/(x-2) × (x+2)(x-2)/﹣8x
=﹣(x+2)/2
再将x的值代入即可(x 的值没写清楚,剩下的你自己做吧!)
=4x(x+3)/(x+3)(x-2)÷[(x-2)²-(x+2)²]/(x+2)(x-2)
=4x/(x-2) ÷[(x-2+x+2)(x-2-x-2)]/(x+2)(x-2)
=4x/(x-2) ÷2x(﹣4)/(x+2)(x-2)
=4x/(x-2) × (x+2)(x-2)/﹣8x
=﹣(x+2)/2
再将x的值代入即可(x 的值没写清楚,剩下的你自己做吧!)
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