A=B:C
\(B=\dfrac{x}{x^2-4}+\dfrac{x}{2-x}+\dfrac{1}{x+2}=\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x-2}+\dfrac{1}{x+2}\)
\(B=\dfrac{x-2\left(x+2\right)+\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-2x-4+x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{-6}{\left(x-2\right)\left(x+2\right)}\)
\(C=\left(x-2\right)+\dfrac{10-x^2}{x+2}=\dfrac{x^2-4+10-x^2}{x+2}=\dfrac{6}{x+2}\)
\(A=B.\dfrac{1}{C}=\dfrac{-6}{\left(x-2\right)\left(x+2\right)}.\dfrac{\left(x+2\right)}{6}\)
a)
\(A=\left\{{}\begin{matrix}\left|x\right|\ne2\\\dfrac{1}{2-x}\end{matrix}\right.\)
\(A\left(\dfrac{1}{2}\right)=\dfrac{1}{2-\dfrac{1}{2}}=\dfrac{1}{\dfrac{3}{2}}=\dfrac{2}{3}\)
\(A\left(-\dfrac{1}{2}\right)=\dfrac{1}{2+\dfrac{1}{2}}=\dfrac{2}{5}\)
b) \(A< 0\Rightarrow2-x< 0\Rightarrow x>2\)
