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We are given the equation:

\[
\frac{3}{2 - \sqrt{5}} = p + q \sqrt{r}
\]

and we need to find the value of \( p - q + r \).

### Step 1: Rationalize the denominator
We will rationalize the denominator of the left-hand side by multiplying both the numerator and denominator by the conjugate of \( 2 - \sqrt{5} \), which is \( 2 + \sqrt{5} \).

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

The denominator simplifies as follows:

\[
(2 - \sqrt{5})(2 + \sqrt{5}) = 2^2 - (\sqrt{5})^2 = 4 - 5 = -1
\]

So the equation becomes:

\[
\frac{3(2 + \sqrt{5})}{-1} = -3(2 + \sqrt{5}) = -6 - 3\sqrt{5}
\]

### Step 2: Compare with \( p + q\sqrt{r} \)
We now compare the expression \( -6 - 3\sqrt{5} \) with \( p + q\sqrt{r} \). This gives us:

- \( p = -6 \)
- \( q = -3 \)
- \( r = 5 \)

### Step 3: Calculate \( p - q + r \)

\[
p - q + r = -6 - (-3) + 5 = -6 + 3 + 5 = 2
\]

Thus, the value of \( p - q + r \) is \( 2 \).

The correct answer is **d. 2**.

Would you like further details or have any questions?

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Here are 5 related questions for practice:
1. How do you rationalize a denominator containing a square root?
2. What is the conjugate of \( 3 + \sqrt{7} \)?
3. What is the simplified result of \( \frac{4}{3 - \sqrt{2}} \)?
4. If \( p + q\sqrt{r} = -8 - 4\sqrt{7} \), what are the values of \( p \), \( q \), and \( r \)?
5. How do you solve an equation involving radicals in both the numerator and denominator?

**Tip:** Rationalizing the denominator is useful when dealing with expressions involving square roots in the denominator, especially when trying to simplify or compare terms.

Jika 3 / (2 - √5) = p + q√r, nilai dari p - q + r adalah...

This problem involves rationalizing a denominator and comparing it to a standard form p + q√r. The detailed solution shows how to simplify and calculate p - q + r. Suitable for students in Grades 10-12.

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