(x+3)/(x+2)-(x+5)/(x+4)=(x+7)/(x+6)-(x+9)/(x+8)
1+1/(x+2)-1-1/(x+4)=1+1/(x+6)-1-1/(x+8)
1/(x+2)-1/(x+4)=1/(x+6)-1/(x+8)
1/(x+2)+1/(x+8)=1/(x+4)+1/(x+6)
(x+2+x+8)/[(x+2)(x+8)]=(x+4+x+6)/[(x+4)(x+6)]
(2x+10)/(x^2+10x+16)=(2x+10)/(x^2+10x+24)
由于x^2+10x+16恒≠x^2+10x+24,要等式成立,只有2x+10=0
x=-5
仅有一个解.