\(\dfrac{1}{x+2}-\dfrac{7}{x-2}=\dfrac{2x-5}{x^2-4}\)
ĐKXĐ:\(\left[{}\begin{matrix}x-2\ne0\\x+2\ne0\end{matrix}\right.\Leftrightarrow x\ne\pm2\)
\(\dfrac{1}{x+2}-\dfrac{7}{x-2}=\dfrac{2x-5}{x^2-4}\)
\(\Leftrightarrow\dfrac{1\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x-5}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow x-2-7x-14=2x-5\)
\(\Leftrightarrow x-7x-2x=-5+2+14\)
\(\Leftrightarrow-8x=11\)
\(\Leftrightarrow x=\dfrac{-11}{8}\)
\(\dfrac{1}{x+2}-\dfrac{7}{x-2}=\dfrac{2x-5}{x^2-4}\\ ĐKXĐ:x+2\ne0\\ \Leftrightarrow x\ne-2\\ x-2\ne0\\ \Leftrightarrow x\ne2\)
\(\Leftrightarrow\dfrac{1}{x+2}-\dfrac{7}{x-2}=\dfrac{2x-5}{\left(x+2\right)\left(x-2\right)}\\ \Leftrightarrow x-2-7\left(x+2\right)=2x-5\\ \Leftrightarrow x-2-7x-14=2x-5\\ \Leftrightarrow x-2-7x-14-2x+5=0\\ \Leftrightarrow-8x-11=0\\ \Leftrightarrow-8x=11\\ \Leftrightarrow x=-\dfrac{11}{8}\)
