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Limits Calculator

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1

Here, we show you a step-by-step solved example of limits. This solution was automatically generated by our smart calculator:

$\lim_{x\to\:5}\left(\frac{x^2-25}{x-5}\right)$

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 $5$

$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
2

Factor the difference of squares $x^2-25$ as the product of two conjugated binomials

$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
3

Simplify the fraction $\frac{\left(x+5\right)\left(x-5\right)}{x-5}$ by $x-5$

$x+5$
4

Evaluate the limit $\lim_{x\to5}\left(x+5\right)$ by replacing all occurrences of $x$ by $5$

$5+5$
5

Add the values $5$ and $5$

$10$

Final answer to the problem

$10$

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