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Find the limit of $3x^2-x-10=8$ as $x$ approaches $-2$

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Solution

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Step-by-step Solution

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  • Solve without using l'Hôpital
  • Write in simplest form
  • Solve using L'Hôpital's rule
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Evaluate the limit

$\lim_{x\to-2}\left(3x^2-x-10\right)=8$

Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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