Limit of $[\ln (3+x^2) - \ln (2+x)]$ as $x$ approaches $\infty$ I got an answer as $\infty$ but I need more clear explanation.
Please help me!

Hint:
You can use equivalents, and the properties of log:
$$\ln(3+x^2)-\ln(1+x)=\ln \frac{x^2+3}{x+1}.$$
On the other hand,
$$\frac{x^2+3}{x+1}\sim_\infty \frac{x^2}x=\ln x\enspace\text{so}\quad\ln(3+x^2)-\ln(1+x)\sim_\infty \ln x.$$
