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

Step-by-step Solution

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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 without using l'Hôpital
  • Solve using L'Hôpital's rule
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Factor the polynomial $x^2-x$ by it's greatest common factor (GCF): $x$

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

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

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

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^2+x+-2)/(x^2-x) as x approaches 1. Factor the polynomial x^2-x by it's greatest common factor (GCF): x. Factor the trinomial x^2+x-2 finding two numbers that multiply to form -2 and added form 1. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Simplifying.

Final answer to the problem

$3$

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Function Plot

Plotting: $\frac{x^2+x-2}{x^2-x}$

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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

How to improve your answer:

Main Topic: Limits by Direct Substitution

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

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