# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve limits problems step by step online.

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

Learn how to solve limits problems step by step online. Evaluate the limit of ((10-x)^0.5-4)/(x+6) as x approaches -6. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{10-x}-4\right)\left(\sqrt{10-x}+4\right). Evaluate the limit by replacing all occurrences of x by -6.

$-\infty$

### Problem Analysis

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

Limits

~ 0.1 seconds