\(\dfrac{x+3}{x+2}+\dfrac{x}{2-x}=\dfrac{5x}{x^2-4}\)
\(\Leftrightarrow\dfrac{x+3}{x+2}-\dfrac{x}{x-2}=\dfrac{5x}{\left(x-2\right)\left(x+2\right)}\)
ĐKXĐ : \(\left\{{}\begin{matrix}x+2\ne0\\x-2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-2\\x\ne2\end{matrix}\right.\)
Ta có : \(\dfrac{x+3}{x+2}-\dfrac{x}{x-2}=\dfrac{5x}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\dfrac{\left(x+3\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{5x}{\left(x-2\right)\left(x+2\right)}\)
`=> x^2 -2x +3x-6 - x^2 -2x -5x=0`
`<=>-6x -6=0`
`<=>-6x=6`
`<=>x=-1(t/m)`
=>(x+3)(x-2)-x(x+2)=5x
=>x^2+x-6-x^2-2x=5x
=>5x=-x-6
=>6x=-6
=>x=-1
