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To solve this problem, we need to rationalize the denominator of the fraction:

\[
\frac{4}{\sqrt{5} - \sqrt{3}}
\]

### Step 1: Multiply by the Conjugate
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of \(\sqrt{5} - \sqrt{3}\) is \(\sqrt{5} + \sqrt{3}\). So we multiply as follows:

\[
\frac{4}{\sqrt{5} - \sqrt{3}} \times \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}} = \frac{4(\sqrt{5} + \sqrt{3})}{(\sqrt{5} - \sqrt{3})(\sqrt{5} + \sqrt{3})}
\]

### Step 2: Simplify the Denominator
The denominator is now a difference of squares:

\[
(\sqrt{5})^2 - (\sqrt{3})^2 = 5 - 3 = 2
\]

Thus, the expression becomes:

\[
\frac{4(\sqrt{5} + \sqrt{3})}{2}
\]

### Step 3: Simplify the Fraction
Now, divide both the numerator and denominator by 2:

\[
\frac{4(\sqrt{5} + \sqrt{3})}{2} = 2(\sqrt{5} + \sqrt{3})
\]

### Final Answer:
The simplified expression is \( 2(\sqrt{5} + \sqrt{3}) \), which corresponds to option **b** in the question.

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Would you like any further explanation or details?

Here are 5 related questions to explore:
1. How do you multiply radicals with different bases?
2. What are other examples of conjugates in rationalizing denominators?
3. Can the same method be applied for rationalizing higher-degree roots?
4. How do you simplify the product of two binomials involving square roots?
5. What happens if both the numerator and denominator contain radicals?

**Tip:** Always check for opportunities to use conjugates when dealing with irrational denominators!

Jika penyebut pecahan 4 / (√5 - √3) sama dengan _____?

Learn how to rationalize the denominator of 4 / (√5 - √3) by multiplying by the conjugate. This problem explores key algebraic concepts including radical expressions and the difference of squares theorem. Suitable for students in Grades 9-11.

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