\(P=\left(\dfrac{2+x}{2-x}+\dfrac{4x^2}{x^2-4}-\dfrac{2-x}{2+x}\right):\dfrac{x^2-3x}{2x^2-x^3}\)
a). ĐKXĐ: \(x\ne0;\pm2\)
b).
\(P=\left(\dfrac{2+x}{2-x}+\dfrac{4x^2}{x^2-4}-\dfrac{2-x}{2+x}\right):\dfrac{x^2-3x}{2x^2-x^3}\)
\(P=\left[-\dfrac{\left(x+2\right)^2}{x^2-4}+\dfrac{4x^2}{x^2-4}+\dfrac{\left(x-2\right)^2}{x^2-4}\right]:\dfrac{x-3}{2x-x^2}\)
\(P=\left(\dfrac{-x^2-4x-4+4x^2+x^2-4x+4}{x^2-4}\right):\dfrac{x-3}{2x-x^2}\)
\(P=\dfrac{4x^2-8x}{x^2-4}:\dfrac{x-3}{2x-x^2}=\dfrac{\left(4x^2-8x\right)\left(2x-x^2\right)}{\left(x^2-4\right)\left(x-3\right)}\)
\(P=\dfrac{8x^3-4x^4-16x^2+8x^3}{\left(x+2\right)\left(x-2\right)\left(x-3\right)}=\dfrac{16x^3-4x^4-16x^2}{\left(x+2\right)\left(x-2\right)\left(x-3\right)}\)
\(P=\dfrac{-4x^2\left(-4x+x^2+4\right)}{\left(x+2\right)\left(x-2\right)\left(x-3\right)}=\dfrac{-4x^2\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)\left(x-3\right)}\)
\(P=\dfrac{-4x^2\left(x-2\right)}{\left(x+2\right)\left(x-3\right)}\)
c).
\(\left|x-5\right|=2\Rightarrow\)\(\left[{}\begin{matrix}x-5=2\\x-5=-2\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=3\end{matrix}\right.\)
thay lần lượt các giá trị của x vào P, ta được:
\(\left[{}\begin{matrix}P=\dfrac{-4.\left(7\right)^2\left(7-2\right)}{\left(7+2\right)\left(7-3\right)}\\P=\dfrac{-4.\left(3\right)^2.\left(3-2\right)}{\left(3+2\right)\left(3-3\right)}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}P=-\dfrac{245}{9}\\\text{P không xác định }\end{matrix}\right.\)
