Evaluating a limit by factoring

👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time.
The limit of a function is usually evaluated by direct substitution of the value which the variable tends to. When the function is a rational expression such that direct substitution leads to zero in the denominator, we find a way to either eliminate the denominator by multiplying both the numerator and the denominator by a common factor or decompose the denominator and the numerator into constituent parts so that like terms can cancel out.
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Organized Videos:
✅The Limit
• The Limit
✅Evaluate Limits of Complex Fractions
• Evaluate Limits of Com...
✅Evaluate Limits of Polynomials
• Evaluate Limits of Pol...
✅Evaluate Limits of Rational Expressions
• Evaluate Limits of Rat...
✅Evaluate Limits with Square Roots
• Evaluate Limits with S...
✅Evaluate Limits with Trig
• Evaluate Limits with Trig
✅Limits of Piecewise Functions
• Limits of Piecewise Fu...
✅Evaluate Limits with Transcendentals
• Evaluate Limits with T...
✅Evaluate Limits Difference Quotient
• Evaluate Limits Differ...
✅Evaluate Limits from a Graph
• Evaluate Limits from a...
✅Evaluate Limits of Absolute Value
• Evaluate Limits of Abs...
✅Evaluate Limits of Square Root
• Evaluate Limits of Squ...
✅Holes and Asymptotes of Rational Functions
• Holes and Asymptotes o...
✅Learn about Limits
• Learn about Limits
✅Find the Value that makes the Function Continuous
• Find the Value that ma...
✅Is the Functions Continuous or Not?
• Is the Functions Conti...
✅Evaluate Limits using a Table of Values
• Evaluate Limits using ...
✅Evaluate Limits at Infinity
• Evaluate Limits at Inf...
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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvideos.com/about-me/

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substitution failed, for a function I am working on, therefore I did factoring and it also failed, what should I do?

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Where did (x+3) (x+1) come from?

[@iBe_Vybin]

Factoring the equation. Another way you could look at it is ”what two numbers multiple to 3, and add up to 4”. Thinking about it like that, you would get values 3 and 1, which is where (x+3) (x+1) came from