Question

解方程 x+2分之x+3加x+3分之x+4=x+4分之x+5加x+1分之x+2

Answer 1

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

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

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

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

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

x²+3x+2=x²+7x+12

x=-5/2

检验：x=-5/2是方程的解