Limits by factoring Calculator

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Difficult Problems

1

Solved example of limits by factoring

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

Applying the power of a power property

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

Simplify the fraction $\frac{\left(x+4\right)\left(x-4\right)}{\left(x-4\right)\left(x+6\right)}$ by $x-4$

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

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

$\lim_{x\to4}\left(\frac{x+4}{x+6}\right)$
3

Evaluate the limit by replacing all occurrences of $x$ by $4$

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

Add the values $4$ and $6$

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

Add the values $4$ and $4$

$\frac{8}{10}$

Divide $8$ by $10$

$\frac{4}{5}$
4

Simplifying

$\frac{4}{5}$

$\frac{4}{5}$