# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

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. Evaluate the limit of ((x+6)^0.5-4)/(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). Simplify the fraction \frac{-10+x}{\left(x-10\right)\left(\sqrt{x+6}+4\right)} by -10+x.

$\frac{1}{8}$$\,\,\left(\approx 0.125\right)$
$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$