Try NerdPal! Our new app on iOS and Android

# Find the limit of $\frac{\sqrt{x+3}-2}{x^2-1}$ as $x$ approaches $1$

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

$\frac{1}{8}$$\,\,\left(\approx 0.125\right) Got another answer? Verify it here ## Step-by-step Solution Problem to solve: \lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right) Choose the solving method 1 Applying rationalisation \lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}\right) Learn how to solve limits by factoring problems step by step online. \lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}\right) Learn how to solve limits by factoring problems step by step online. Find the limit of ((x+3)^0.5-2)/(x^2-1) as x approaches 1. Applying rationalisation. Multiplying fractions \frac{\sqrt{x+3}-2}{x^2-1} \times \frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}. Solve the product of difference of squares \left(\sqrt{x+3}-2\right)\left(\sqrt{x+3}+2\right). Expand and simplify -1+x. ## Final Answer \frac{1}{8}$$\,\,\left(\approx 0.125\right)$
SnapXam A2

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

### Tips on how to improve your answer:

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right)$

### Main topic:

Limits by factoring

~ 0.08 s