$$\frac{2x+3}{8}-\frac{x+4}{x+2}=\frac{5+3x}{x-2}$$
$x=\frac{-\sqrt{1513}\cos(\frac{\arccos(\frac{55133\sqrt{1513}}{2289169})}{3})-\sqrt{4539}\sin(\frac{\arccos(\frac{55133\sqrt{1513}}{2289169})}{3})+29}{6}\approx -2.938107157$
$x=\frac{2\sqrt{1513}\cos(\frac{\arccos(\frac{55133\sqrt{1513}}{2289169})}{3})+29}{6}\approx 17.707205105$
$x=\frac{\sqrt{4539}\sin(\frac{\arccos(\frac{55133\sqrt{1513}}{2289169})}{3})-\sqrt{1513}\cos(\frac{\arccos(\frac{55133\sqrt{1513}}{2289169})}{3})+29}{6}\approx -0.269097948$
