Final Answer
$\frac{1}{8}$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$
Specify the solving method
1
Applying rationalisation
$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right)$
Learn how to solve limits problems step by step online.
$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right)$
Learn how to solve limits problems step by step online. Find the limit of ((x+6)^1/2-4)/(x-10) as x approaches 10. Applying rationalisation. Multiplying fractions \frac{\sqrt{x+6}-4}{x-10} \times \frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}. Solve the product of difference of squares \left(\sqrt{x+6}-4\right)\left(\sqrt{x+6}+4\right). Expand and simplify -10+x.
Final Answer
$\frac{1}{8}$
Numeric Answer
$0.125$