[tex]{8\,x^{3}+4\,x^{2}+2\,x+1\neq 0,\;\;16\,x^{4}-1\neq 0}\\\dfrac{8\,x+29}{16\,x^{4}-1}+\dfrac{18\,x+5}{8\,x^{3}+4\,x^{2}+2\,x+1}=\dfrac{25}{4\,x^{2}+1}\Leftrightarrow \left(4\,x^{2}+1\right)\,\left(\dfrac{8\,x+29}{16\,x^{4}-1}+\dfrac{18\,x+5}{8\,x^{3}+4\,x^{2}+2\,x+1}\right)=25\\x^2=t,t > 0\Rightarrow \dfrac{36\,t+24}{4\,t-1}=25\Leftrightarrow 36\,t+24=25\,\left(4\,t-1\right)\Rightarrow t=\dfrac{49}{64}\Rightarrow x=\pm \frac{7}{8}[/tex]