Question

初二因式分解难题

Answer 1

1/x(x+1)+1/(x+1)(x+2）+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
(x+2+x)/x+(x+1)+(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
2(x+1)/x(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
2/x(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
[2(x+3)+x]/x(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
3(x+2)/x(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
3/x(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
[3(x+4)+x]/x(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
4(x+3)/x(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
4/x(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
[4(x+5)+x]/x(x+4)(x+5)=5/(x²+11x-708)
5(x+4)/x(x+4)(x+5)=5/(x²+11x-708)
5/x(x+5)=5/(x²+11x-708)
x(x+5)=x²+11x-708
x²+5x=x²+11x-708
6x=708
x=118

Answer 2

1/x(x+1) +1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x²+11x-708)
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=5/(x²+11x-708)
1/x-1/(x+5)=5/(x²+11x-708)
(x+5-x)/x(x+5)=5/(x²+11x-708)
x(x+5)=x²+11x-708
-6x=-708
x=118