Final Answer
$10$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to 5}\left(\frac{x^2-25}{x-5}\right)$
Specify the solving method
1
The difference of the squares of two terms, divided by the difference of the same terms, is equal to the sum of the terms, in other words:
- $\displaystyle\frac{a^2-b^2}{a-b}=a+b$
- Where the value of $a$ is $x$
- and the value of $b$ is $5$, therefore:
- The fraction $\frac{x^2-25}{x-5}$ simplified equals $x+5$
$\lim_{x\to5}\left(x+5\right)$
2
Evaluate the limit $\lim_{x\to5}\left(x+5\right)$ by replacing all occurrences of $x$ by $5$
$5+5$
Add the values $5$ and $5$
$10$
3
Simplifying, we get
$10$
Final Answer
$10$