# Binomial conjugates Calculator

## Get detailed solutions to your math problems with our Binomial conjugates 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 Binomial conjugates

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

$\frac{36}{161}$