ĐKXĐ:\(x\ne\pm2\)
\(\dfrac{x}{x-2}-\dfrac{5}{x+2}+\dfrac{12}{4-x^2}=1\\ \Leftrightarrow\dfrac{x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{5\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{12}{\left(x+2\right)\left(x-2\right)}-\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x^2+2x-5x+10-12-x^2+4}{\left(x+2\right)\left(x-2\right)}=0\\ \Rightarrow-3x+2=0\\ \Leftrightarrow x=\dfrac{2}{3}\left(tm\right)\)
\(\Leftrightarrow x\left(x+2\right)-5\left(x-2\right)-12=x^2-4\)
\(\Leftrightarrow x^2+2x-5x+10-12=x^2-4\)
=>-3x-2=-4
=>-3x=-2
hay x=2/3(nhận)
