Final answer to the problem
$10$
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Step-by-step Solution
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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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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 $\frac{1}{2}$
$\frac{\left(x+\sqrt{25}\right)\left(\sqrt{x^2}-\sqrt{25}\right)}{x-5}$
Calculate the power $\sqrt{25}$
$\frac{\left(x+5\right)\left(\sqrt{x^2}-\sqrt{25}\right)}{x-5}$
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 $\frac{1}{2}$
$\frac{\left(x+5\right)\left(x-\sqrt{25}\right)}{x-5}$
Calculate the power $\sqrt{25}$
$\frac{\left(x+5\right)\left(x- 5\right)}{x-5}$
Multiply $-1$ times $5$
$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
1
Factor the difference of squares $x^2-25$ as the product of two conjugated binomials
$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
2
Simplify the fraction $\frac{\left(x+5\right)\left(x-5\right)}{x-5}$ by $x-5$
$x+5$
3
Evaluate the limit $\lim_{x\to5}\left(x+5\right)$ by replacing all occurrences of $x$ by $5$
$5+5$
4
Add the values $5$ and $5$
$10$
Final answer to the problem
$10$
