Question

解方程：1/（x的平方+x）+1/（x的平方+3x+2）+1/（x的平方+5x+6）+1/（x的平方+7x+12）=4/21

Answer 1

化简：
(1/x)*(1/(x+1))+(1/(x+1))*(1/(x+2))+(1/(x+2))*(1/(x+3))+(1/(x+3))*(1/(x+4))=4/21

(1/x)-(1/(x+1))+(1/(x+1))-(1/(x+2))+(1/(x+2))-(1/(x+3))+(1/(x+3))-(1/(x+4))=4/21

(1/x)*(1/(x+4))=1/21

x=3

Answer 2

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)=4/21
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=4/21
1/x-1/(x+4)=4/21
两边乘21x(x+4)
21(x+4)-21x=4x(x+4)
x²+4x-21=0
(x+7)(x-3)=0
x=-7,x=3
分式方程要检验
经检验，x=-7，x=3是方程的解

Answer 3

＝1/x(x+1)+1/(x+1)(x+2)+1/(x+3)(x+2)+1/(x+4)(x+3)
=2/x(x+2)+2/(x+2)(x+4)
=2/x(x+2)