Neither 6n+75 and 2n+109 converges so we must rearrange the expression so that both numerator and denominator converge.

Divide through by n

\lim\limits_{n\to \infty} \dfrac{6n+75}{2n+109}

= \lim\limits_{n\to \infty} \dfrac{6+\dfrac{75}{n} }{2+\dfrac{109}{n} }

=\dfrac{ \lim\limits_{n\to \infty}6+\dfrac{75}{n} }{ \lim\limits_{n\to \infty}2+\dfrac{109}{n}} //apply algebra of limits

=\dfrac{6+0}{2+0}

=3