Question

Find the limit.....
$\displaystyle{ \lim _{x \to5} \frac{ {x}^{2} - 5}{ {x}^{2} + x - 30 } }$
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Answer 1

Answer:

10/11

Step-by-step explanation:

${ \lim _{x \to5} \frac{ {x}^{2} - 5}{ {x}^{2} + x - 30 } } \\

{\lim _{x \to5} \frac{ (x + 5)(x - 5)}{ {x}^{2} + 6x - 5x - 30 } } \\

{\lim _{x \to5} \frac{ (x + 5)(x - 5)}{x( x + 6) - 5 (x + 6)} } \\

{\lim _{x \to5} \frac{ (x + 5)(x - 5)}{( x + 6)(x - 5)} } \\{\lim _{x \to5}} \frac{x + 5}{x + 6} \\ \frac{5 + 5}{5 + 6} \\ \frac{10}{11}$