(x+3)/(x+2)+(x+4)/(x+3)=(x+5)/(x+4)+(x+2)/(x+1),求x

问题描述:

(x+3)/(x+2)+(x+4)/(x+3)=(x+5)/(x+4)+(x+2)/(x+1),求x
要巧算,急.

(x+3)/(x+2)=1+1/(x+2) (x+4)/(x+3)=1+1/(x+3) (x+5)/(x+4)=1+1/(x+4) (x+2)/(x+1)=1+1/(x+1) 则原式可化简为1/(x+2)+1/(x+3)=1/(x+4)+1/(x+1),两边通分得(2x+5)/(x+2)(x+3)=(2x+5)/(x+1)(x+4) 若x=-2.5,则原式成立; 当x不等于-2.5,则(x+2)(x+3)=(x+1)(x+4) 展开,方程无意义 则x=-2.5