ĐKXĐ: \(\left\{{}\begin{matrix}4x-20\ne0\\50-2x^2\ne0\\6x+30\ne0\end{matrix}\right.\)=> \(\left\{{}\begin{matrix}4x-20\ne0\\x^2-25\ne0\\6x+30\ne0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}x-5\ne0\\x+5\ne0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x\ne5\\x\ne-5\end{matrix}\right.\)
=> \(x\ne\pm5\)
Ta có : \(\frac{3}{4x-20}+\frac{15}{50-2x^2}+\frac{7}{6x+30}=0\)
=> \(\frac{3}{4\left(x-5\right)}-\frac{15}{2\left(x-5\right)\left(x+5\right)}+\frac{7}{6\left(x+5\right)}=0\)
=> \(\frac{9\left(x+5\right)}{12\left(x^2-25\right)}-\frac{90}{12\left(x^2-25\right)}+\frac{14\left(x-5\right)}{12\left(x^2-25\right)}=0\)
=> \(9\left(x+5\right)-90+14\left(x-5\right)=0\)
=> \(9x+45-90+14x-70=0\)
=> \(23x=115\)
=> \(x=5\) ( KTM )
Vậy phương trình vô nghiệm .
