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

## Step-by-step Solution

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### Videos

$10$
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## Step-by-step Solution

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 $5$

$5+5$

Add the values $5$ and $5$

$10$
3

Simplifying, we get

$10$

$10$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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