?$解:?\frac {x+1}{x+2}-\frac {x+2}{x+3}=\frac {x+5}{x+6}-\frac {x+6}{x+7}?$?
?$? \frac {(x+1)(x+3)-(x+2)^2}{(x+2)(x+3)}=\frac {(x+5)(x+7)-(x+6)^2}{(x+6)(x+7)}?$?
?$? \frac {-1}{(x+2)(x+3)}=\frac {-1}{(x+6)(x+7)}?$?
?$ ∴?(x+2)(x+3)=(x+6)(x+7),?化簡(jiǎn)得?5x+6=13x+42?$?
?$? x=-\frac 92?$?
?$ 經(jīng)檢驗(yàn),?x=-\frac 92?是原方程式的解$?