# Step-by-step Solution

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$\frac{1}{8}$$\,\,\left(\approx 0.125\right) Got a different answer? Try our new Answer Assistant! ## Step-by-step Solution Problem to solve: \lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right) Choose the solving method 1 Applying rationalisation \lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right) Learn how to solve limits problems step by step online. \lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right) Learn how to solve limits problems step by step online. Find the limit of ((x+6)^0.5-4)/(x-10) as x approaches 10. Applying rationalisation. Multiplying fractions \frac{\sqrt{x+6}-4}{x-10} \times \frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}. Solve the product of difference of squares \left(\sqrt{x+6}-4\right)\left(\sqrt{x+6}+4\right). Simplify the fraction \frac{-10+x}{\left(x-10\right)\left(\sqrt{x+6}+4\right)} by -10+x. ## Final Answer \frac{1}{8}$$\,\,\left(\approx 0.125\right)$
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sin
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tan
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coth
sech
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asinh
acosh
atanh
acoth
asech
acsch

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