\(P=\dfrac{2+x}{x-2}+\dfrac{2}{x+2}-\dfrac{2x^2}{4-x^2}\)
\(=\dfrac{x+2}{x-2}+\dfrac{2}{x+2}+\dfrac{2x^2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)^2+2\left(x-2\right)+2x^2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+4x+4+2x-4+2x^2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{3x^2+6x}{\left(x-2\right)\left(x+2\right)}=\dfrac{3x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{3x}{x-2}\)
e: P<3
=>\(\dfrac{3x}{x-2}< 3\)
=>\(\dfrac{x}{x-2}< 1\)
=>\(\dfrac{x}{x-2}-1< 0\)
=>\(\dfrac{x-x+2}{x-2}< 0\)
=>\(\dfrac{2}{x-2}< 0\)
=>x-2<0
=>x<2
Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}x< 2\\x\ne-2\end{matrix}\right.\)