Try NerdPal! Our new app on iOS and Android

# Find the limit of $\frac{x^2+4x-21}{x-3}$ as $x$ approaches $3$

## Step-by-step Solution

Go!
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

### Videos

The limit does not exist

## Step-by-step Solution

Problem to solve:

$\lim_{x\to3}\left(\frac{x^2+4x-21}{x-3}\right)$

Specify the solving method

1

Expand the fraction $\frac{x^2+4x-21}{x-3}$

$\lim_{x\to3}\left(\frac{x^2}{x-3}+\frac{4x}{x-3}+\frac{-21}{x-3}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to3}\left(\frac{x^2}{x-3}+\frac{4x}{x-3}+\frac{-21}{x-3}\right)$

Learn how to solve limits problems step by step online. Find the limit of (x^2+4x-21)/(x-3) as x approaches 3. Expand the fraction \frac{x^2+4x-21}{x-3}. The limit of a sum of two or more 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)). The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Evaluate the limit \lim_{x\to3}\left(\frac{x^2}{x-3}\right) by replacing all occurrences of x by 3.

The limit does not exist

### Explore different ways to solve this problem

Limits by direct substitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing
$\lim_{x\to3}\left(\frac{x^2+4x-21}{x-3}\right)$

Limits

~ 0.14 s