Final answer to the problem
$-5\sqrt{13}$
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Step-by-step Solution
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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- 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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1
Applying rationalisation
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$\lim_{x\to3}\left(\frac{x^2-x-6}{\sqrt{3x+4}-\sqrt{5x-2}}\frac{\sqrt{3x+4}+\sqrt{5x-2}}{\sqrt{3x+4}+\sqrt{5x-2}}\right)$
Learn how to solve problems step by step online. Find the limit of (x^2-x+-6)/((3x+4)^(1/2)-(5x-2)^(1/2)) as x approaches 3. Applying rationalisation. Multiplying fractions \frac{x^2-x-6}{\sqrt{3x+4}-\sqrt{5x-2}} \times \frac{\sqrt{3x+4}+\sqrt{5x-2}}{\sqrt{3x+4}+\sqrt{5x-2}}. Solve the product of difference of squares \left(\sqrt{3x+4}-\sqrt{5x-2}\right)\left(\sqrt{3x+4}+\sqrt{5x-2}\right). Combining like terms 3x and -5x.
Final answer to the problem
$-5\sqrt{13}$
