Question

Find the limit.....


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

Answer 1

10/11

Explanation:

`{ \lim _(x \to5) \frac{ {x}^(2) - 5}{ {x}^(2) + x - 30 } } \\ </p><p>{\lim _(x \to5) \frac{ (x + 5)(x - 5)}{ {x}^(2) + 6x - 5x - 30 } } \\ </p><p>{\lim _(x \to5) ( (x + 5)(x - 5))/(x( x + 6) - 5 (x + 6)) } \\ </p><p>{\lim _(x \to5) ( (x + 5)(x - 5))/(( x + 6)(x - 5)) } \\{\lim _(x \to5)} (x + 5)/(x + 6) \\ (5 + 5)/(5 + 6) \\ (10)/(11)`