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
Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$
$\lim_{x\to5}\left(\frac{\left(x+5\right)\left(x-5\right)}{x-5}\right)$
1
Factor the difference of squares $x^2-25$ as the product of two conjugated binomials
$\lim_{x\to5}\left(\frac{\left(x+5\right)\left(x-5\right)}{x-5}\right)$
2
Simplify the fraction $\frac{\left(x+5\right)\left(x-5\right)}{x-5}$ by $x-5$
$\lim_{x\to5}\left(x+5\right)$
3
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 $5$
$10$
4
Simplifying, we get
$10$
Final Answer
$10$