Question

Solve it (Easy question) :
$\lim_{x \rightarrow 1} \cfrac{x {}^{2} - 25 }{x {}^{2} - 5 }$
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Answer 1

The solution to the limit expression $\lim_{x \to 1} \frac{x^2 - 25}{x - 5}$ is 6

The limit expression is given as:

$\lim_{x \to 1} \frac{x^2 - 25}{x - 5}$

Express 25 as 5^2

$\lim_{x \to 1} \frac{x^2 - 5^2}{x - 5}$

Express the numerator as the difference of two squares

$\lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} \frac{(x - 5)(x +5)}{x - 5}$

Evaluate the quotient

$\lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} (x +5)$

Remove bracket

$\lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} x +5$

Substitute 1 for x

$\lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 1 +5$

$\lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 6$

Hence, the solution to the limit expression $\lim_{x \to 1} \frac{x^2 - 25}{x - 5}$ is 6

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