Question

Answer 1

ĐKXĐ:\(x\ne\pm2\)

\(\dfrac{x-2}{x+2}-\dfrac{3}{x-2}=\dfrac{2\left(x-11\right)}{x^2-4}\\ \Leftrightarrow\dfrac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}-\dfrac{3\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{2x-22}{\left(x+2\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x^2-4x+4-3x-6-2x+22}{\left(x+2\right)\left(x-2\right)}=0\\ \Rightarrow x^2-9x+20=0\\\Leftrightarrow \left(x-4\right)\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4\left(tm\right)\\x=5\left(tm\right)\end{matrix}\right.\)