https://file.aiquickdraw.com/mathbot/file/1727054098221mf4xqdfe.jpg

To simplify the expression given in the image:

\[
\frac{\sqrt{8} - \sqrt{6}}{\sqrt{8} + \sqrt{6}}
\]

using the method of rationalizing the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \(\sqrt{8} + \sqrt{6}\) is \(\sqrt{8} - \sqrt{6}\).

So, multiply both the numerator and denominator by \(\sqrt{8} - \sqrt{6}\):

\[
\frac{\sqrt{8} - \sqrt{6}}{\sqrt{8} + \sqrt{6}} \times \frac{\sqrt{8} - \sqrt{6}}{\sqrt{8} - \sqrt{6}}
\]

This gives:

\[
\frac{(\sqrt{8} - \sqrt{6})^2}{(\sqrt{8})^2 - (\sqrt{6})^2}
\]

Now simplify:

1. **Numerator:**
\[
(\sqrt{8} - \sqrt{6})^2 = (\sqrt{8})^2 - 2\sqrt{8}\sqrt{6} + (\sqrt{6})^2 = 8 - 2\sqrt{48} + 6 = 14 - 2\sqrt{48}
\]

Since \(\sqrt{48} = 4\sqrt{3}\), the numerator becomes:
\[
14 - 8\sqrt{3}
\]

2. **Denominator:**
\[
(\sqrt{8})^2 - (\sqrt{6})^2 = 8 - 6 = 2
\]

Now, the expression becomes:
\[
\frac{14 - 8\sqrt{3}}{2}
\]

Finally, simplify by dividing both terms in the numerator by 2:
\[
7 - 4\sqrt{3}
\]

Thus, the simplified expression is:

\[
7 - 4\sqrt{3}
\]

Would you like a detailed explanation of any of the steps?

---

Here are five related questions for further practice:

1. How do you simplify \(\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}\) using rationalization?
2. What is the conjugate of \(\sqrt{a} + \sqrt{b}\), and why is it used in rationalization?
3. How would you rationalize \(\frac{1}{\sqrt{2} + \sqrt{3}}\)?
4. What is the simplified result of \(\frac{\sqrt{10} - \sqrt{2}}{\sqrt{10} + \sqrt{2}}\)?
5. Can you apply rationalization to a denominator of the form \(a + b\sqrt{c}\)? How?

**Tip:** When rationalizing, always multiply by the conjugate of the denominator to eliminate radicals.

Sederhanakan bentuk pecahan berikut dengan cara merasionalkan penyebutnya: (√8 - √6) / (√8 + √6)

Learn how to simplify the expression (√8 - √6) / (√8 + √6) using the rationalization method. This step-by-step guide covers key algebraic concepts such as simplifying radicals and rationalizing denominators. Suitable for students in Grades 10-12.

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