# Factor by difference of squares Calculator

## Get detailed solutions to your math problems with our Factor by difference of squares step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

1

Solved example of Factor by difference of squares

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$
2

Applying rationalisation

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\cdot\frac{\sqrt{5+x}+\sqrt{5}}{\sqrt{5+x}+\sqrt{5}}\right)$
3

Multiplying fractions

$\lim_{x\to0}\left(\frac{\left(\sqrt{5+x}-\sqrt{5}\right)\left(\sqrt{5+x}+\sqrt{5}\right)}{x\left(\sqrt{5+x}+\sqrt{5}\right)}\right)$
4

Solve the product $\left(\sqrt{5+x}-\sqrt{5}\right)\left(\sqrt{5+x}+\sqrt{5}\right)$

$\lim_{x\to0}\left(\frac{\left(\sqrt{5+x}\right)^2-5}{x\left(\sqrt{5+x}+\sqrt{5}\right)}\right)$
5

Applying the power of a power property

$\lim_{x\to0}\left(\frac{5+x-5}{x\left(\sqrt{5+x}+\sqrt{5}\right)}\right)$
6

Subtract the values $5$ and $-5$

$\lim_{x\to0}\left(\frac{x+0}{x\left(\sqrt{5+x}+\sqrt{5}\right)}\right)$
7

$x+0=x$, where $x$ is any expression

$\lim_{x\to0}\left(\frac{x}{x\left(\sqrt{5+x}+\sqrt{5}\right)}\right)$
8

Simplifying the fraction by $x$

$\lim_{x\to0}\left(\frac{1}{\sqrt{5+x}+\sqrt{5}}\right)$
9

Evaluating the limit when $x$ tends to $0$

$\frac{1}{\sqrt{5+0}+\sqrt{5}}$
10

Simplifying

$\frac{36}{161}$

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