Find the limit of $\frac{\left(2x+3\right)\sqrt{x-1}}{2x^2+x-3}$ as $x$ approaches $1$

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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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Multiplying polynomials $\sqrt{x-1}$ and $2x+3$

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$\lim_{x\to1}\left(\frac{2\sqrt{x-1}x+3\sqrt{x-1}}{2x^2+x-3}\right)$

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Learn how to solve problems step by step online. Find the limit of ((2x+3)(x-1)^(1/2))/(2x^2+x+-3) as x approaches 1. Multiplying polynomials \sqrt{x-1} and 2x+3. Applying rationalisation. Multiply and simplify the expression within the limit. The power of a product is equal to the product of it's factors raised to the same power.

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Function Plot

Plotting: $\frac{\left(2x+3\right)\sqrt{x-1}}{2x^2+x-3}$

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