Step-by-step Solution

Evaluate the limit of $\frac{\sqrt{x+3}-2}{x^2-1}$ as $x$ approaches $1$

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Step-by-step explanation

Problem to solve:

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

Learn how to solve limits by factoring problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve limits by factoring problems step by step online. Evaluate the limit of ((x+3)^0.5-2)/(x^2-1) as x approaches 1. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{x+3}-2\right)\left(\sqrt{x+3}+2\right). Factor the difference of squares \left(x^2-1\right) as the product of two conjugated binomials.

Final Answer

$\frac{1}{8}$$\,\,\left(\approx 0.125\right)$

Problem Analysis

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

Main topic:

Limits by factoring

Time to solve it:

~ 0.08 seconds