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# Find the limit of $\frac{x^2+8x-9}{x^3-x^2+5x-5}$ as $x$ approaches $5$

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##  Final answer to the problem

$\frac{7}{15}$
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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
Can't find a method? Tell us so we can add it.
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We can factor the polynomial $x^3-x^2+5x-5$ using the rational root theorem, which guarantees that for a polynomial of the form $a_nx^n+a_{n-1}x^{n-1}+\dots+a_0$ there is a rational root of the form $\pm\frac{p}{q}$, where $p$ belongs to the divisors of the constant term $a_0$, and $q$ belongs to the divisors of the leading coefficient $a_n$. List all divisors $p$ of the constant term $a_0$, which equals $-5$

$1, 5$

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

$1, 5$

Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^2+8x+-9)/(x^3-x^25x+-5) as x approaches 5. We can factor the polynomial x^3-x^2+5x-5 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -5. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3-x^2+5x-5 will then be. Trying all possible roots, we found that 1 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

##  Final answer to the problem

$\frac{7}{15}$

$0.4667$

##  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

SnapXam A2

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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.