Step-by-step Solution

Evaluate the limit of $\frac{x^2-25}{x-5}$ as $x$ approaches $5$

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Final Answer

$10$

Step-by-step explanation

Problem to solve:

$\lim_{x\to\:5}\left(\frac{x^2-25}{x-5}\right)$

Choose the solving method

1

The difference of the squares of two terms, divided by the difference of the same terms, is equal to the sum of the terms, in other words:

  • $\displaystyle\frac{a^2-b^2}{a-b}=a+b$
  • Where the value of $a$ is $x$
  • and the value of $b$ is $5$, therefore:
  • The fraction $\frac{x^2-25}{x-5}$ simplified equals $x+5$

$\lim_{x\to5}\left(x+5\right)$
2

Evaluate the limit $\lim_{x\to5}\left(x+5\right)$ by replacing all occurrences of $x$ by $5$

$5+5$
3

Simplifying, we get

$10$

Final Answer

$10$
$\lim_{x\to\:5}\left(\frac{x^2-25}{x-5}\right)$

Main topic:

Limits by factoring

Time to solve it:

~ 0.02 s (SnapXam)