\(ĐKXĐ:x\ne\pm2\)
\(\frac{x}{x+2}+\frac{6}{2-x}=\frac{3x-12}{x^2-4}\)
\(\Leftrightarrow\frac{x}{x+2}-\frac{6}{x-2}-\frac{3x-12}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{x\left(x-2\right)-6\left(x+2\right)-\left(3x-12\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow x^2-2x-6x-12-3x+12=0\)
\(\Leftrightarrow x^2-11x=0\)
\(\Leftrightarrow x\left(x-11\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-11=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=11\end{cases}}\)(tm)
Vậy tập nghiệm của phương trình là \(S=\left\{0;11\right\}\)
\(ĐKXĐ:x\ne\pm2\)
\(\frac{x}{x+2}+\frac{6}{2-x}=\frac{3x-12}{x^2-4}\)
\(\Leftrightarrow\frac{x}{x+2}+\frac{-6}{x-2}-\frac{3x-12}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{x\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{-6\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{3x-12}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{x\left(x-2\right)-6\left(x+2\right)-\left(3x-12\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow x\left(x-2\right)-6\left(x+2\right)-\left(3x-12\right)=0\)
\(\Leftrightarrow x^2-2x-6x-12-3x+12=0\)
\(\Leftrightarrow x^2-11x=0\)\(\Leftrightarrow x\left(x-11\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-11=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=11\end{cases}}\)( thoả mãn \(ĐKXĐ\))
Vậy tập nghiệm của phương trình là \(S=\left\{0;11\right\}\)
