Question

8.5 divide radical expressions (homework)
score: 8/14 answered: 9/14
question 10
rationalize the denominator:
\\(\frac{4}{\sqrt{x}+\sqrt{6}}=\\)
question help: video written example
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Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $\sqrt{x}-\sqrt{6}$.
$\frac{4}{\sqrt{x}+\sqrt{6}}\times\frac{\sqrt{x}-\sqrt{6}}{\sqrt{x}-\sqrt{6}}$

Step2: Expand denominator

Use $(a + b)(a - b)=a^{2}-b^{2}$ for denominator.
$\frac{4(\sqrt{x}-\sqrt{6})}{(\sqrt{x})^{2}-(\sqrt{6})^{2}}$

Step3: Simplify

Simplify the denominator.
$\frac{4(\sqrt{x}-\sqrt{6})}{x - 6}$

Answer:

$\frac{4(\sqrt{x}-\sqrt{6})}{x - 6}$