a.
\(B=\dfrac{5x-2}{\left(x-2\right)\left(x+2\right)}-\dfrac{3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{5x-2-3\left(x-2\right)+x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+4x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x+2}{x-2}\)
b.
\(\left|x+3\right|=5\Rightarrow\left[{}\begin{matrix}x+3=5\\x+3=-5\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\left(ktm\right)\\x=-8\end{matrix}\right.\)
\(\Rightarrow x=-8\)
\(\Rightarrow P=\dfrac{-8+2}{-8-2}=\dfrac{-6}{-10}=\dfrac{3}{5}\)
c.
\(P=\dfrac{x-2+4}{x-2}=1+\dfrac{4}{x-2}\)
\(P\in Z\Rightarrow\dfrac{4}{x-2}\in Z\Rightarrow x-2=Ư\left(4\right)\)
\(\Rightarrow x-2=\left\{-4;-2;-1;1;2;4\right\}\)
\(\Rightarrow x=\left\{-2;0;1;3;4;6\right\}\)
