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. 

Let $\epsilon>0$,
$$\left|u_n-\frac{3}{2}\right|=\left|\frac{3n^2+4}{2n^2+5}-\frac{3}{2}\right|=\frac{7}{4n^2+10}<\epsilon\iff 4n^2>\frac{7}{\epsilon}-10$$
so let $N=\frac{1}{2}\sqrt{\left|\frac{7}{\epsilon}-10\right|}$ then forall $n>N$ we have $\left|u_n-\frac{3}{2}\right|<\epsilon$ and we conclude.
