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# Find the limit $\lim_{x\to3}\left(\frac{x^2+4x-21}{x-3}\right)$

## Step-by-step Solution

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$10$
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##  Step-by-step Solution 

Problem to solve:

$\lim_{x\to3}\left(\frac{x^2+4x-21}{x-3}\right)$

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Factor the trinomial $x^2+4x-21$ finding two numbers that multiply to form $-21$ and added form $4$

$\begin{matrix}\left(-3\right)\left(7\right)=-21\\ \left(-3\right)+\left(7\right)=4\end{matrix}$

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

$\begin{matrix}\left(-3\right)\left(7\right)=-21\\ \left(-3\right)+\left(7\right)=4\end{matrix}$

Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(3)lim((x^2+4x-21)/(x-3)). Factor the trinomial x^2+4x-21 finding two numbers that multiply to form -21 and added form 4. Thus. Simplifying. Evaluate the limit \lim_{x\to3}\left(x+7\right) by replacing all occurrences of x by 3.

$10$

##  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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a
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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

~ 0.04 s

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