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# Find the limit $\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$

## Step-by-step Solution

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###  Solution

$\frac{7}{15}$
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##  Step-by-step Solution 

Problem to solve:

$\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$

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Evaluate the limit $\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$ by replacing all occurrences of $x$ by $5$

$\frac{5^2+8\cdot 5-9}{5^3-1\cdot 5^2+5\cdot 5-5}$

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$\frac{5^2+8\cdot 5-9}{5^3-1\cdot 5^2+5\cdot 5-5}$

Learn how to solve problems step by step online. Find the limit (x)->(5)lim((x^2+8x-9)/(x^3-x^25x-5)). Evaluate the limit \lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right) by replacing all occurrences of x by 5. Multiply 5 times 5. Subtract the values 25 and -5. Multiply 8 times 5.

$\frac{7}{15}$

$0.4667$

##  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

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

SnapXam A2

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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

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