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# Find the limit $\lim_{x\to3}\left(\frac{x^2-5x+6}{x-3}\right)$

## Step-by-step Solution

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##  Step-by-step Solution 

Problem to solve:

$\lim_{x\to3}\left(\frac{x^2-5x+6}{x-3}\right)$

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Factor the trinomial $x^2-5x+6$ finding two numbers that multiply to form $6$ and added form $-5$

$\begin{matrix}\left(-2\right)\left(-3\right)=6\\ \left(-2\right)+\left(-3\right)=-5\end{matrix}$

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

$\begin{matrix}\left(-2\right)\left(-3\right)=6\\ \left(-2\right)+\left(-3\right)=-5\end{matrix}$

Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(3)lim((x^2-5x+6)/(x-3)). Factor the trinomial x^2-5x+6 finding two numbers that multiply to form 6 and added form -5. Thus. Simplifying. Evaluate the limit \lim_{x\to3}\left(x-2\right) by replacing all occurrences of x by 3.

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##  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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(◻)
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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

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