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# Find the limit of $\frac{9x}{x-1}+\frac{-9}{\ln\left(x\right)}$ as $x$ approaches $1$

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##  Final answer to the problem

$\frac{9}{2}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve using L'Hôpital's rule
• Solve without using l'Hôpital
• 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
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1

The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

$L.C.M.=\left(x-1\right)\ln\left(x\right)$

Learn how to solve problems step by step online.

$L.C.M.=\left(x-1\right)\ln\left(x\right)$

Learn how to solve problems step by step online. Find the limit of (9x)/(x-1)+-9/ln(x) as x approaches 1. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Simplify the numerators. Combine and simplify all terms in the same fraction with common denominator \left(x-1\right)\ln\left(x\right).

##  Final answer to the problem

$\frac{9}{2}$

##  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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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