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Limits by factoring Calculator

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1

Solved example of limits by factoring

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

Applying the power of a power property

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

Applying the power of a power property

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

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

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

Solve the product of difference of squares $\left(x+1\right)\left(x-1\right)$

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right)$
4

Solve the product $\left(x+1\right)\left(x-1\right)$

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2+0x-1}\right)$
5

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

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

Applying the power of a power property

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

Applying the power of a power property

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{\left(1+x\right)\left(1-x\right)}\right)$
6

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

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

Add the values $1$ and $3$

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

Multiply $-1$ times $1$

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

The square root of $4$ is $2$

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

Subtract the values $2$ and $-2$

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

Add the values $1$ and $1$

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

Subtract the values $1$ and $-1$

$\frac{0}{2\cdot 0}$

Multiply $2$ times $0$

$\frac{0}{0}$

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

indeterminate
7

Simplifying

indeterminate

Answer

indeterminate

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