# Find the limits lim_{yrightarrow2}frac{y+2}{y^2+5y+6}

Tahmid Knox 2020-12-24 Answered
Find the limits
$\underset{y\to 2}{lim}\frac{y+2}{{y}^{2}+5y+6}$
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tabuordy
Given that,
$\underset{y\to 2}{lim}\frac{y+2}{{y}^{2}+5y+6}$
Plug the value y=2,
$\underset{y\to 2}{lim}\frac{y+2}{{y}^{2}+5y+6}=\frac{2+2}{\left({2}^{2}\right)+5\left(2\right)+6}$
$=\frac{4}{4+10+6}$
$=\frac{4}{20}$
$=\frac{1}{5}$
Therefore,
$\underset{y\to 2}{lim}\frac{y+2}{{y}^{2}+5y+6}=\frac{1}{5}$