[Graph]

\(\displaystyle{\frac{{{x}+{3}}}{{{x}+{2}}}}={\frac{{{x}}}{{{x}+{2}}}}+{\frac{{{3}}}{{{x}+{2}}}}\). It has a vertical asymptote at x=-2. \(\displaystyle{\frac{{{3}}}{{{x}+{2}}}}\) is dominant near the asymptote, and \(\displaystyle{\frac{{{x}}}{{{x}+{2}}}}\) is dominant as x goes to \(\displaystyle\infty\) or \(\displaystyle-\infty\). (It has the same horizontal asymptote, y=1.

\(\displaystyle{\frac{{{x}+{3}}}{{{x}+{2}}}}={\frac{{{x}}}{{{x}+{2}}}}+{\frac{{{3}}}{{{x}+{2}}}}\). It has a vertical asymptote at x=-2. \(\displaystyle{\frac{{{3}}}{{{x}+{2}}}}\) is dominant near the asymptote, and \(\displaystyle{\frac{{{x}}}{{{x}+{2}}}}\) is dominant as x goes to \(\displaystyle\infty\) or \(\displaystyle-\infty\). (It has the same horizontal asymptote, y=1.