Câu 1:
a) ĐKXĐ: \(x\ne\pm2,x\ne-10\)
b) \(P=\dfrac{\left(x+5\right)\left(x+2\right)+3x\left(x-2\right)-4x^2}{\left(x-2\right)\left(x+2\right)}.\dfrac{x\left(x+2\right)}{x+10}\)
\(=\dfrac{x+10}{\left(x-2\right)\left(x+2\right)}.\dfrac{x\left(x+2\right)}{x+10}=\dfrac{x}{x-2}\)
c) \(x^2-x-6=0\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-2\left(ktm\right)\end{matrix}\right.\)
\(P=\dfrac{x}{x-2}=\dfrac{3}{3-2}=3\)
Câu 2:
a) ĐKXĐ: \(x\ne\pm3,x\ne-\dfrac{1}{2}\)
\(A=\dfrac{\left(x-1\right)\left(x-3\right)+2\left(x+3\right)-x^2-3}{\left(x-3\right)\left(x+3\right)}.\dfrac{2x+1}{-2}\)
\(=\dfrac{-2x+6}{\left(x-3\right)\left(x+3\right)}.\dfrac{2x+1}{-2}=\dfrac{-2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}.\dfrac{2x+1}{-2}=\dfrac{2x+1}{x+3}\)
b) \(\left|x-2\right|=1\Leftrightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=3\left(ktm\right)\\x=1\left(tm\right)\end{matrix}\right.\)
\(A=\dfrac{2x+1}{x+3}=\dfrac{2.1+1}{1+3}=\dfrac{3}{4}\)
c) \(A=\dfrac{2x+1}{x+3}>0\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}2x+1>0\\x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1< 0\\x+3< 0\end{matrix}\right.\end{matrix}\right.\\x\ne\pm3,x\ne-\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>-\dfrac{1}{2},x\ne3\\x< -3\end{matrix}\right.\)
d) \(A=\dfrac{2x+1}{x+3}=\dfrac{2\left(x+3\right)-5}{x+3}=2-\dfrac{5}{x+3}\in Z\)
\(\Leftrightarrow\left(x+3\right)\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\Leftrightarrow x\in\left\{-8;-4;-2;2\right\}\)
Mà A nhận giá trị nhỏ nhất \(\Rightarrow x+3=1\Leftrightarrow x=-2\left(tm\right)\)
1 lần chỉ nên đăng 1-2 bài thôi nhé bạn !
