a) \(P=\dfrac{5x-2-3\left(x-2\right)+x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2+4x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x+2}{x-2}\)
b) \(\left|x+3\right|=5\)\(\Rightarrow\left[{}\begin{matrix}x+3=5\\x+3=-5\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=2\left(ktm\right)\\x=-8\left(tm\right)\end{matrix}\right.\)
\(P=\dfrac{x+2}{x-2}=\dfrac{-8+2}{-8-2}=\dfrac{3}{5}\)
c) \(P=\dfrac{x+2}{x-2}=\dfrac{x-2+4}{x-2}=1+\dfrac{4}{x-2}\in Z\)
\(\Rightarrow\left(x-2\right)\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
Kết hợp ĐKXĐ:
\(\Rightarrow x\in\left\{0;1;3;4;6\right\}\)
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