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

## Step-by-step Solution

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$3$
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##  Step-by-step Solution 

Problem to solve:

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

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1

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 direct substitution 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 direct substitution problems step by step online. Find the limit (x)->(5)lim((x^2-7x+10)/(x-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

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

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a
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u
v
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x
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(◻)
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◻/◻
/
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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

~ 0.03 s

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