Question

\(\dfrac{5}{x+2}-\dfrac{x-1}{2-x}=\dfrac{12}{x^2-4}+1\)

Answer 1

ĐKXĐ:\(x\ne\pm2\)

\(\dfrac{5}{x+2}-\dfrac{x-1}{2-x}=\dfrac{12}{x^2-4}+1\\ \Leftrightarrow\dfrac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{12}{\left(x-2\right)\left(x+2\right)}-\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=0\\ \Leftrightarrow\dfrac{5x-10+x^2+x-2-12-x^2+4}{\left(x-2\right)\left(x+2\right)}=0\\ \Rightarrow6x-20=0\\ \Leftrightarrow x=\dfrac{10}{3}\left(tm\right)\)

Answer 2