Question

Answer 1

ĐKXĐ:\(x\ne\pm2\)

\(\dfrac{x-4}{x+2}-\dfrac{x+1}{x-2}=\dfrac{24}{x^2-4}\\ \Leftrightarrow\dfrac{\left(x-2\right)\left(x-4\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{24}{\left(x-2\right)\left(x+2\right)}=0\\ \Leftrightarrow\dfrac{x^2-6x+8-x^2-3x-2-24}{\left(x-2\right)\left(x+2\right)}=0\\ \Rightarrow-9x-18=0\\ \Leftrightarrow x=-2\left(ktm\right)\)

Answer 2

\(\Leftrightarrow\left(x-4\right)\left(x-2\right)-\left(x+1\right)\left(x+2\right)=24\)

\(\Leftrightarrow x^2-6x+8-x^2-3x-2=24\)

=>-9x+6=24

=>-9x=18

hay x=-2(loại)