先化简分式(x+3)/(x^2-1)÷(x^2+6x+9)/(x^2-2x+1)+1/(x+1),再去适当的x的值代入取

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先化简分式(x+3)/(x^2-1)÷(x^2+6x+9)/(x^2-2x+1)+1/(x+1),再去适当的x的值代入取
先化简分式(x+3)/(x^2-1)÷(x^2+6x+9)/(x^2-2x+1)+1/(x+1),再去适当的x的值代入取

先化简分式(x+3)/(x^2-1)÷(x^2+6x+9)/(x^2-2x+1)+1/(x+1),再去适当的x的值代入取
原式=[(x+3)/(x²-1)]÷[(x²+6x+9)/(x²-2x+1)]+1/(x+1)
={(x+3)/[(x-1)(x+1)]÷[(x+3)²/(x-1)²]+1/(x+1)
={(x+3)/[(x-1)(x+1)]}×[(x-1)²/(x+3)²]+1/(x+1)
=(x-1)/[(x+1)(x+3)]+1/(x+1)
=(x-1)/[(x+1)(x+3)]+(x+3)/[(x+1)(x+3)]
=(x-1+x+3)/[(x+1)(x+3)]
=(2x+2)/[(x+1)(x+3)]
=2(x+1)/[(x+1)(x+3)]
=2/(x+3)
当x=2时
原式=2/(2+3)=2/5