1/x的平方+3x+2+1/x的平方+5x+6+1/x的平方+4x+3

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1/x的平方+3x+2+1/x的平方+5x+6+1/x的平方+4x+3
1/x的平方+3x+2+1/x的平方+5x+6+1/x的平方+4x+3

1/x的平方+3x+2+1/x的平方+5x+6+1/x的平方+4x+3
1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+4x+3)
=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+1)(x+3)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+1)(x+3)
=1/(x+1)-1/(x+3)+1/(x+1)(x+3)
=(x+3)/(x+1)(x+3)-(x+1)/(x+1)(x+3)+1/(x+1)(x+3)
=[(x+3)-(x+1)]/(x+1)(x+3)+1/(x+1)(x+3)
=2/(x+1)(x+3)+1/(x+1)(x+3)
=3/(x+1)(x+3)
=3/(x^2+4x+3)

1/x的平方+3x+2+1/x的平方+5x+6+1/x的平方+4x+3 =1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=1/(x+1)-1/(x+4)=1/(x^2+5x+4)

1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+4x+3)
=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+1)(x+3)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/2(x+1)-1/2(x+3)
=1/(x+1)-1/(x+3)+1/2(x+1)-1/2(x+3)
=3/2(x+1)-3/2(x+3)
=3/(x+1)(x+3)
=3/(x^2+4x+3)