神马作文网(6x+12)/(x^2+4x+4)+(4-x^2)/(x^2-4x+4)=(x^2)/(4-x^2)
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/09/29 17:29:23
(6x+12)/(x^2+4x+4)+(4-x^2)/(x^2-4x+4)=(x^2)/(4-x^2)
哎呦亲们帮帮忙吧.我受不了了
哎呦亲们帮帮忙吧.我受不了了
化简左式：
(6x+12)/(x^2+4x+4)+(4-x^2)/(x^2-4x+4)
=6(x+2)/(x+2)²+(2+x)(2-x)/(x-2)²
=6/(x+2)-(x+2)/(x-2)
=6(x-2)/[(x+2)(x-2)]-(x+2)²/[(x+2)(x-2)]
=6(x+2)/(x²-4)-(x+2)²/(x²-4)
=(2x-x²-16)/(x²-4)
=(x²-2x+16)/(4-x²)
∵左式=右式
∴(x²-2x+16)/(4-x²)=x²/(4-x²)=
∴x²-2x+16=x²
∴x=8
(6x+12)/(x^2+4x+4)+(4-x^2)/(x^2-4x+4)
=6(x+2)/(x+2)²+(2+x)(2-x)/(x-2)²
=6/(x+2)-(x+2)/(x-2)
=6(x-2)/[(x+2)(x-2)]-(x+2)²/[(x+2)(x-2)]
=6(x+2)/(x²-4)-(x+2)²/(x²-4)
=(2x-x²-16)/(x²-4)
=(x²-2x+16)/(4-x²)
∵左式=右式
∴(x²-2x+16)/(4-x²)=x²/(4-x²)=
∴x²-2x+16=x²
∴x=8
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