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# Limits by Factoring Calculator

## Get detailed solutions to your math problems with our Limits by Factoring step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of limits by factoring. This solution was automatically generated by our smart calculator:

$\lim_{x\to4}\left(\frac{x^2-16}{x^2+2x-24}\right)$
2

Factor the trinomial $x^2+2x-24$ finding two numbers that multiply to form $-24$ and added form $2$

$\begin{matrix}\left(-4\right)\left(6\right)=-24\\ \left(-4\right)+\left(6\right)=2\end{matrix}$
3

Thus

$\lim_{x\to4}\left(\frac{x^2-16}{\left(x-4\right)\left(x+6\right)}\right)$

Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$

$\lim_{x\to4}\left(\frac{\left(x+\sqrt{16}\right)\left(\sqrt{x^2}-\sqrt{16}\right)}{\left(x-4\right)\left(x+6\right)}\right)$

Calculate the power $\sqrt{16}$

$\lim_{x\to4}\left(\frac{\left(x+4\right)\left(\sqrt{x^2}-\sqrt{16}\right)}{\left(x-4\right)\left(x+6\right)}\right)$

Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$

$\lim_{x\to4}\left(\frac{\left(x+4\right)\left(x-\sqrt{16}\right)}{\left(x-4\right)\left(x+6\right)}\right)$

Calculate the power $\sqrt{16}$

$\lim_{x\to4}\left(\frac{\left(x+4\right)\left(x- 4\right)}{\left(x-4\right)\left(x+6\right)}\right)$

Multiply $-1$ times $4$

$\lim_{x\to4}\left(\frac{\left(x+4\right)\left(x-4\right)}{\left(x-4\right)\left(x+6\right)}\right)$
4

Factor the difference of squares $x^2-16$ as the product of two conjugated binomials

$\lim_{x\to4}\left(\frac{\left(x+4\right)\left(x-4\right)}{\left(x-4\right)\left(x+6\right)}\right)$
5

Simplify the fraction

$\lim_{x\to4}\left(\frac{x+4}{x+6}\right)$
6

Evaluate the limit $\lim_{x\to4}\left(\frac{x+4}{x+6}\right)$ by replacing all occurrences of $x$ by $4$

$\frac{4+4}{4+6}$
7

Add the values $4$ and $6$

$\frac{4+4}{10}$
8

Add the values $4$ and $4$

$\frac{8}{10}$
9

Divide $8$ by $10$

$\frac{4}{5}$

##  Final answer to the problem

$\frac{4}{5}$

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