Answer
$=\dfrac {5}{3}$
Work Step by Step
Recall:
(1) $\lim _{x\rightarrow c}\dfrac {f\left( x\right) }{g\left( x\right) }=\dfrac {\lim _{x\rightarrow c}f\left( x\right) }{\lim _{x\rightarrow c}g\left( x\right) }$
(2) $\lim _{x\rightarrow c}f(x) = f(c)$
Use the rules above to have:
$\Rightarrow \lim _{x\rightarrow 2}\dfrac {3x+4}{x^{2}+x}
\\=\dfrac {\lim _{x\rightarrow 2}\left( 3x+4\right) }{\lim _{x\rightarrow 2}\left( x^{2}+x\right) }
\\=\dfrac {3\times 2+4}{2^{2}+2}
\\=\dfrac {10}{6}
\\=\dfrac {5}{3}$
