Prove that the sequence $(3n^2+4)/(2n^2+5) $ converges to $3/2$ 
Prove directly from the definition that the sequence $\left( \dfrac{3n^2+4}{2n^2+5} \right)$ converges to $\dfrac{3}{2}$.

I know that the definition of a limit of a sequence is $|a_n - L| < \varepsilon$ .
However I do not know how to prove this using this definition. 
Any help is kindly appreciated. 

The following computation proves the claim
$$\left|\frac{3}{2}-\frac{3n^2 + 4}{2n^2+5}\right| = \left|\frac{(6n^2+15)-(6n^2+8)}{4n^2+10}\right| = \left|\frac{7}{4n^2+10}\right|\stackrel{n\rightarrow\infty}{\longrightarrow}0$$
The same computation shows that in general if you have two polynomials $P$ and $Q$ of the same degree $m$, then $\frac{P(n)}{Q(n)}$ converges to $\frac{p_m}{q_m}$, where $p_m$ is the coefficient of $x^m$ in $P$ and similarly for $Q$.
