Question

解方程:(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)+(1/x

Answer 1

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=1/8

1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=1/8

1/(x+1)-1/(x+5)=1/8

(x+5-x-1)/(x+1)(x+5)=1/8

32=x²+6x+5

x²+6x-27=0

(x+9)(x-3)=0

x=-9 x=3

检验：x=-9 x=3是方程的解