Question

giải pt;\(\dfrac{x+2}{x-2}-\dfrac{x-3}{x+2}=5\)

Answer 1

\(\dfrac{x+2}{x-2}-\dfrac{x-3}{x+2}=5\\ \Leftrightarrow\dfrac{\left(x+2\right)^2-\left(x-2\right)\left(x-3\right)}{\left(x-2\right)\left(x+2\right)}=5\\ \Leftrightarrow\dfrac{x^2+4x+4-x^2+5x-6}{\left(x^2-4\right)}=5\\ \Leftrightarrow9x-2=5\left(x^2-4\right)\\ \Leftrightarrow5x^2-20=9x-2\\ \Leftrightarrow5x^2-9x-18=0\\ \Leftrightarrow\left(5x+6\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}5x+6=0\\x-3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{6}{5}\\x=3\end{matrix}\right.\)

Vậy \(x\in\left\{-\dfrac{6}{5};3\right\}\)

Answer 2