\(\frac{x^2+y^2+3}{x^2+y^2+2}=\frac{x^2+y^2+2+1}{x^2+y^2+2}=1+\frac{1}{x^2+y^2+2}\le1+\frac{1}{2}=\frac{3}{2}\)
\("="\Leftrightarrow x=y=0\)
\(\frac{x^2+y^2+3}{x^2+y^2+2}\)
\(=\frac{x^2+y^2+2+1}{x^2+y^2+2}\)
\(=1+\frac{1}{x^2+y^2+2}\le1+\frac{1}{2}=\frac{3}{2}\)
\("="\Leftrightarrow x=y=0\)