Final Answer
$\frac{1}{8}$$\,\,\left(\approx 0.125\right)$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right)$
Choose the solving method
1
Applying rationalisation
$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}\right)$
Learn how to solve limits by factoring problems step by step online.
$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}\right)$
Learn how to solve limits by factoring problems step by step online. Find the limit of ((x+3)^0.5-2)/(x^2-1) as x approaches 1. Applying rationalisation. Multiplying fractions \frac{\sqrt{x+3}-2}{x^2-1} \times \frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}. Solve the product of difference of squares \left(\sqrt{x+3}-2\right)\left(\sqrt{x+3}+2\right). Expand and simplify -1+x.
Final Answer
$\frac{1}{8}$$\,\,\left(\approx 0.125\right)$