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

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##  Final answer to the problem

$3$
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##  Step-by-step Solution 

How should I solve this problem?

• Solve the limit using factorization
• Solve using L'Hôpital's rule
• Solve without using l'Hôpital
• Solve using limit properties
• Solve using direct substitution
• Solve the limit using rationalization
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
Can't find a method? Tell us so we can add it.
1

Factor the trinomial $x^2-x-2$ finding two numbers that multiply to form $-2$ and added form $-1$

$\begin{matrix}\left(1\right)\left(-2\right)=-2\\ \left(1\right)+\left(-2\right)=-1\end{matrix}$

Learn how to solve limits by direct substitution problems step by step online.

$\begin{matrix}\left(1\right)\left(-2\right)=-2\\ \left(1\right)+\left(-2\right)=-1\end{matrix}$

Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^2-x+-2)/(x-2) as x approaches 2. Factor the trinomial x^2-x-2 finding two numbers that multiply to form -2 and added form -1. Thus. Simplifying. Evaluate the limit \lim_{x\to2}\left(x+1\right) by replacing all occurrences of x by 2.

##  Final answer to the problem

$3$

$3$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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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

###  Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.