# Step-by-step Solution

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

Go!
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### Videos

$10$

## Step-by-step explanation

Problem to solve:

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

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\lim_{x\to5}\left(x\right)+\lim_{x\to5}\left(5\right)$
3

The limit of a constant is just the constant

$\lim_{x\to5}\left(x\right)+5$
4

Evaluate the limit by replacing all occurrences of $x$ by $5$

$5+5$
5

Add the values $5$ and $5$

$10$

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

Limits

5

### Time to solve it:

~ 0.02 s (SnapXam)