Question

解分式方程：（x+3）/（x+2）+(x+4)/(x+3)=(x+5)/(x+4)+(x+2)/(x+1)

大家帮一下，谢~谢~

Answer 1

解：（x+2+1）/（x+2）+(x+3+1)/(x+3)=(x+4+1)/(x+4)+(x+1+1)/(x+1)，即
1/（x+2）+1/(x+3)=1/(x+4)+1/(x+1),(2x+5)/(x^2+5x+6)=(2x+5)/(x^2+5x+4),即2x+5=0,x=-5/2.检验x=-5/2是方程的解。