Question

Answer 1

\(a,ĐK:x\ne\pm3\\ P=\dfrac{x^2+2x-3+x^2-6x+9+4x-2}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+3-x-1}{x+3}\\ P=\dfrac{2x^2+4}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x+3}{2}=\dfrac{x^2+2}{x-3}\\ b,\left|2x-1\right|=5\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\1-2x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(ktm\right)\\x=-2\left(tm\right)\end{matrix}\right.\\ \Leftrightarrow A=\dfrac{4+2}{-2-3}=-\dfrac{6}{5}\\ c,P=\dfrac{x^2-9+11}{x-3}=x+3+\dfrac{11}{x-3}\in Z\\ \Leftrightarrow x-3\inƯ\left(11\right)=\left\{-11;-1;1;11\right\}\\ \Leftrightarrow x\in\left\{-8;2;4;14\right\}\)