Find the limit of (x^2+7x+10)/(x+5) as x approaches -5

 Exercise

$\lim_{x\to-5}\frac{x^2+7x+10}{x+5}$

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Factor the trinomial $x^2+7x+10$ finding two numbers that multiply to form $10$ and added form $7$

$\begin{matrix}\left(2\right)\left(5\right)=10\\ \left(2\right)+\left(5\right)=7\end{matrix}$

 

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

$\lim_{x\to-5}\left(\frac{\left(x+2\right)\left(x+5\right)}{x+5}\right)$

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Simplifying

$\lim_{x\to-5}\left(x+2\right)$

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Evaluate the limit $\lim_{x\to-5}\left(x+2\right)$ by replacing all occurrences of $x$ by $-5$

$-5+2$

 

Subtract the values $2$ and $-5$

$-3$

$-3$

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