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# Find the limit of $\frac{x^2-7x+10}{x-5}$ as $x$ approaches $5$

## Step-by-step Solution

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$3$
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## Step-by-step Solution

Problem to solve:

$\lim_{x\to5}\left(\frac{x^2-7x+10}{x-5}\right)$

Specify the solving method

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Factor the trinomial $x^2-7x+10$ finding two numbers that multiply to form $10$ and added form $-7$

$\begin{matrix}\left(-2\right)\left(-5\right)=10\\ \left(-2\right)+\left(-5\right)=-7\end{matrix}$

Learn how to solve limits by factoring problems step by step online.

$\begin{matrix}\left(-2\right)\left(-5\right)=10\\ \left(-2\right)+\left(-5\right)=-7\end{matrix}$

Learn how to solve limits by factoring problems step by step online. Find the limit of (x^2-7x+10)/(x-5) as x approaches 5. Factor the trinomial x^2-7x+10 finding two numbers that multiply to form 10 and added form -7. Thus. Simplifying. Evaluate the limit \lim_{x\to5}\left(x-2\right) by replacing all occurrences of x by 5.

$3$

### Explore different ways to solve this problem

Limits by direct substitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing
SnapXam A2

### beta Got another answer? Verify it!

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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

$\lim_{x\to5}\left(\frac{x^2-7x+10}{x-5}\right)$