a.
\(x=1\Rightarrow A=\dfrac{1^2+2}{1+2}=\dfrac{3}{3}=1\)
b.
\(B=\dfrac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{8}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{4x-8+2x+4-8}{\left(x-2\right)\left(x+2\right)}=\dfrac{6x-12}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{6}{x+2}\)
c.
\(M=\dfrac{6}{x+2}.\dfrac{x+2}{x^2+2}=\dfrac{6}{x^2+2}\le\dfrac{6}{2}=3\)
\(M_{max}=3\) khi \(x=0\)
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