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Binomial conjugates Calculator

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1

Solved example of binomial conjugates

$\lim_{x\to-1}\left(\frac{5-\sqrt{3x+28}}{x+1}\right)$
2

Applying rationalisation

$\lim_{x\to-1}\left(\frac{5-\sqrt{3x+28}}{x+1}\cdot\frac{5+\sqrt{3x+28}}{5+\sqrt{3x+28}}\right)$
3

Multiplying fractions

$\lim_{x\to-1}\left(\frac{\left(5-\sqrt{3x+28}\right)\left(5+\sqrt{3x+28}\right)}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
4

Solve the product $\left(5-\sqrt{3x+28}\right)\left(5+\sqrt{3x+28}\right)$

$\lim_{x\to-1}\left(\frac{5^2-\left(\sqrt{3x+28}\right)^2}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
5

Calculate the power $5^2$

$\lim_{x\to-1}\left(\frac{25-\left(\sqrt{3x+28}\right)^2}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
6

Applying the power of a power property

$\lim_{x\to-1}\left(\frac{25-\left(3x+28\right)}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
7

Solve the product $-\left(3x+28\right)$

$\lim_{x\to-1}\left(\frac{25-3x-28}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
8

Subtract the values $25$ and $-28$

$\lim_{x\to-1}\left(\frac{-3-3x}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
9

Factor by the greatest common divisor $3$

$\lim_{x\to-1}\left(\frac{-3\left(1+x\right)}{\left(x+1\right)\left(5+\sqrt{3x+28}\right)}\right)$
10

Simplifying the fraction by $1+x$

$\lim_{x\to-1}\left(\frac{-3}{5+\sqrt{3x+28}}\right)$
11

Evaluating the limit when $x$ tends to $-1$

$\frac{-3}{5+\sqrt{3-1+28}}$
12

Simplifying

$-\frac{3}{10}$

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