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Limits by factoring Calculator

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1

Solved example of limits by factoring

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right)$
2

Factor the difference of squares $x^2-1$ as the product of two conjugated binomials

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{\left(x+1\right)\left(x-1\right)}\right)$

Subtract the values $1$ and $-1$

$\frac{\sqrt{1+3}-2}{0\left(1+1\right)}$

Add the values $1$ and $3$

$\frac{\sqrt{4}-2}{0\left(1+1\right)}$

The square root of $4$ is $2$

$\frac{2-2}{0\left(1+1\right)}$

Any expression multiplied by $0$ is equal to $0$

$\frac{0}{0}$

$\frac{0}{0}$ represents an indeterminate form

indeterminate
3

Simplifying

indeterminate

Answer

indeterminate

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