解方程：[(x+1)/(x+2)]+[(x+2)/(x+3)]=[(x+3)/(x+4)]+[(x+4)/(x+5)]

原方程可化为 [-1/(x+2)]+[-1/(x+3)]=[-1/(x+4)]+[-1/(x+5)] [1/(x+2)]+[1/(x+3)]=[1/(x+4)]+[1/(x+5)] [1/(x+2)(x+3)]=[1/(x+4)(x+5)] (x+2)(x+3)=(x+4)(x+5) x^2+5x+6=x^2+9x+20 -4x=14 x=-7/2 经检验x=-7/2是原方程的根 ∴原方程的根是x=-7/2