ĐKXĐ:\(x\ne5;x\ne-5\)

\(\frac{3}{4x-20}+\frac{15}{50-2x^2}+\frac{7}{6x+30}=0\)

\(\Leftrightarrow\frac{3}{4\left(x-5\right)}+\frac{15}{2\left(25-x^2\right)}+\frac{7}{6\left(x+5\right)}=0\)

\(\Leftrightarrow\frac{9\left(x+5\right)}{12\left(x-5\right)\left(x+5\right)}-\frac{90}{12\left(x-5\right)\left(x+5\right)}+\frac{14\left(x-5\right)}{12\left(x-5\right)\left(x+5\right)}=0\)

\(\Leftrightarrow\frac{9x+45-90+14x-70}{12\left(x-5\right)\left(x+5\right)}=0\)

\(\Leftrightarrow23x-115=0\)

\(\Leftrightarrow x=\frac{115}{23}\)

Tui làm mấy bài giải pt hay sai mấy lỗi cơ bản nhưng đại khái ý tưởng là vậy nha !

\(x=\frac{115}{23}=5\)

vậy pt vô nghiệm

- Ta có: \(\left(x^2-1\right).\left(x+2\right).\left(x-3\right)=\left(x-1\right).\left(x^2-4\right).\left(x+5\right)\)

      \(\Leftrightarrow\left(x-1\right).\left(x+1\right).\left(x+2\right).\left(x-3\right)=\left(x-1\right).\left(x-2\right).\left(x+2\right).\left(x+5\right)\)

      \(\Leftrightarrow\left(x-1\right).\left(x+1\right).\left(x+2\right).\left(x-3\right)-\left(x-1\right).\left(x-2\right).\left(x+2\right).\left(x+5\right)=0\)

      \(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left[\left(x+1\right).\left(x-3\right)-\left(x-2\right).\left(x+5\right)\right]=0\)

      \(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left[\left(x^2-2x-3\right)-\left(x^2+3x-10\right)\right]=0\)

      \(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left(x^2-2x-3-x^2-3x+10\right)=0\)

      \(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left(-5x+7\right)=0\)

+ \(x-1=0\)\(\Leftrightarrow\)\(x=1\left(TM\right)\)

+ \(x+2=0\)\(\Leftrightarrow\)\(x=-2\left(TM\right)\)

+ \(-5x+7=0\)\(\Leftrightarrow\)\(-5x=-7\)\(\Leftrightarrow\)\(x=\frac{7}{5}\left(TM\right)\)

Vậy \(S=\left\{-2,1,\frac{7}{5}\right\}\)