$?解：方程兩邊同時乘以{(2x+5)}^{2}{(2x+1)}^{2}，得$
$ 3{(2x+1)}^{2}+4{(2x+5)}^{2}=7(2x+1)(2x+5)$
$(12{x}^{2}+12x+3)+(16{x}^{2}+80x+100)=28{x}^{2}+84x+35$
$ 92x+103=84x+35$
$ 8x=-68$
$ x=-{\frac {17} {2}}$
$檢驗：當(dāng)x=-{\frac {17} {2}}時，{(2x+5)}^{2}{(2x+1)}^{2}≠0，$
$故x=-{\frac {17} {2}}是原分式方程的解。$
